Indirect Proofs and Inequalities, Geometry

Indirect Proofs and Inequalities

V. Triangle Inequalities : Lecture 3 | 33:30 min

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Indirect Proofs and Inequalities

The three steps to writing an indirect proof:

Assume that the conclusion is false
Show that the assumption leads to a contradiction of the hypothesis or something you know is true, like some fact or theorem
Point out that the assumption must be false, and, therefore, the conclusion must be true

Inequality: For any real numbers a and b, a > b if and only if there is a positive number c such that a = b + c
Properties of Inequality:

Comparison Property: a > b, a < b, a = b
Transitive Property: If a < b and b < c, then a < c
Addition and Subtraction Properties: If a > b, then a + c > b + c, and a – c > b – c
Multiplication and Division Properties: If a > b, then ac > bc, and a/c > b/c

Exterior Angle Inequality Theorem: If an angle is an exterior angle of a triangle, then its measure is greater than the measures of either of its remote interior angles

Indirect Proofs and Inequalities

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

I. Tools of Geometry
	Coordinate Plane	16:41
	Points, Lines and Planes	17:17
	Measuring Segments	31:31
	Midpoints and Segment Congruence	42:26
	Angles	42:34
II. Reasoning & Proof
	Inductive Reasoning	19:00
	Conditional Statements	42:47
	Point, Line, and Plane Postulates	17:24
	Deductive Reasoning	36:03
	Proofs in Algebra: Properties of Equality	44:31
	Proving Segment Relationship	41:02
	Proving Angle Relationships	33:37
III. Perpendicular & Parallel Lines
	Parallel Lines and Transversals	37:35
	Angles and Parallel Lines	41:53
	Slope of Lines	44:06
	Proving Lines Parallel	25:55
	Parallels and Distance	19:48
IV. Congruent Triangles
	Classifying Triangles	28:43
	Measuring Angles in Triangles	44:43
	Exploring Congruent Triangles	26:46
	Proving Triangles Congruent	47:51
	Isosceles and Equilateral Triangles	27:53
V. Triangle Inequalities
	Special Segments in Triangles	43:44
	Right Triangles	26:34
	Indirect Proofs and Inequalities	33:30
	Inequalities for Sides and Angles of a Triangle	17:26
	Triangle Inequality	28:11
	Inequalities Involving Two Triangles	29:36
VI. Quadrilaterals
	Parallelograms	29:11
	Proving Parallelograms	42:43
	Rectangles	29:47
	Squares and Rhombi	39:14
	Trapezoids and Kites	30:48
VII. Proportions and Similarity
	Using Proportions and Ratios	20:10
	Similar Polygons	27:53
	Similar Triangles	34:10
	Parallel Lines and Proportional Parts	24:07
	Parts of Similar Triangles	27:06
VIII. Applying Right Triangles & Trigonometry
	Pythagorean Theorem	21:14
	Geometric Mean	40:59
	Special Right Triangles	37:57
	Ratios in Right Triangles	40:37
	Angles of Elevation and Depression	21:04
	Law of Sines	35:25
	Law of Cosines	52:43
IX. Circles
	Segments in a Circle	22:43
	Angles and Arc	35:24
	Arcs and Chords	21:51
	Inscribed Angles	27:53
	Tangents	26:16
	Secants, Tangents, & Angle Measures	27:50
	Special Segments in a Circle	23:08
	Equations of Circles	27:01
X. Polygons & Area
	Polygons	27:24
	Area of Parallelograms	17:46
	Area of Triangles Rhombi, & Trapezoids	20:31
	Area of Regular Polygons & Circles	36:43
	Perimeter & Area of Similar Figures	18:17
	Geometric Probability	38:40
XI. Solids
	Three-Dimensional Figures	23:39
	Surface Area of Prisms and Cylinders	38:50
	Surface Area of Pyramids and Cones	26:10
	Volume of Prisms and Cylinders	21:59
	Volume of Pyramids and Cones	22:02
	Surface Area and Volume of Spheres	14:46
	Congruent and Similar Solids	16:06
XII. Transformational Geometry
	Mapping	14:12
	Reflections	23:17
	Translations	18:43
	Rotations	21:26
	Dilation	37:06

Mathematics: Geometry

I. Tools of Geometry
	Coordinate Plane			16:41
		Intro		0:00
		The Coordinate System		0:12
			Coordinate Plane: X-axis and Y-axis	0:15
			Quadrants	1:02
			Origin	2:00
			Ordered Pair	2:17
		Coordinate Plane		2:59
			Example: Writing Coordinates	3:01
		Coordinate Plane, cont.		4:15
			Example: Graphing & Coordinate Plane	4:17
			Collinear	5:58
		Extra Example 1: Writing Coordinates & Quadrants		7:34
		Extra Example 2: Quadrants		8:52
		Extra Example 3: Graphing & Coordinate Plane		10:58
		Extra Example 4: Collinear		12:50
	Points, Lines and Planes			17:17
		Intro		0:00
		Points		0:07
			Definition and Example of Points	0:09
		Lines		0:50
			Definition and Example of Lines	0:51
		Planes		2:59
			Definition and Example of Planes	3:00
		Drawing and Labeling		4:40
			Example 1: Drawing and Labeling	4:41
			Example 2: Drawing and Labeling	5:54
			Example 3: Drawing and Labeling	6:41
			Example 4: Drawing and Labeling	8:23
		Extra Example 1: Points, Lines and Planes		10:19
		Extra Example 2: Naming Figures		11:16
		Extra Example 3: Points, Lines and Planes		12:35
		Extra Example 4: Draw and Label		14:44
	Measuring Segments			31:31
		Intro		0:00
		Segments		0:06
			Examples of Segments	0:08
		Ruler Postulate		1:30
			Ruler Postulate	1:31
		Segment Addition Postulate		5:02
			Example and Definition of Segment Addition Postulate	5:03
		Segment Addition Postulate		8:01
			Example 1: Segment Addition Postulate	8:04
			Example 2: Segment Addition Postulate	11:15
		Pythagorean Theorem		12:36
			Definition of Pythagorean Theorem	12:37
		Pythagorean Theorem, cont.		15:49
			Example: Pythagorean Theorem	15:50
		Distance Formula		16:48
			Example and Definition of Distance Formula	16:49
		Extra Example 1: Find Each Measure		20:32
		Extra Example 2: Find the Missing Measure		22:11
		Extra Example 3: Find the Distance Between the Two Points		25:36
		Extra Example 4: Pythagorean Theorem		29:33
	Midpoints and Segment Congruence			42:26
		Intro		0:00
		Definition of Midpoint		0:07
			Midpoint	0:10
		Midpoint Formulas		1:30
			Midpoint Formula: On a Number Line	1:45
			Midpoint Formula: In a Coordinate Plane	2:50
		Midpoint		4:40
			Example: Midpoint on a Number Line	4:43
		Midpoint		6:05
			Example: Midpoint in a Coordinate Plane	6:06
		Midpoint		8:28
			Example 1	8:30
			Example 2	13:01
		Segment Bisector		15:14
			Definition and Example of Segment Bisector	15:15
		Proofs		17:27
			Theorem	17:53
			Proof	18:21
		Midpoint Theorem		19:37
			Example: Proof & Midpoint Theorem	19:38
		Extra Example 1: Midpoint on a Number Line		23:44
		Extra Example 2: Drawing Diagrams		26:25
		Extra Example 3: Midpoint		29:14
		Extra Example 4: Segment Bisector		33:21
	Angles			42:34
		Intro		0:00
		Angles		0:05
			Angle	0:07
			Ray	0:23
			Opposite Rays	2:09
		Angles		3:22
			Example: Naming Angle	3:23
		Angles		6:39
			Interior, Exterior, Angle	6:40
			Measure and Degrees	7:38
		Protractor Postulate		8:37
			Example: Protractor Postulate	8:38
		Angle Addition Postulate		11:41
			Example: Angle addition Postulate	11:42
		Classifying Angles		14:10
			Acute Angle	14:16
			Right Angles	14:30
			Obtuse Angle	14:41
		Angle Bisector		15:02
			Example: Angle Bisector	15:04
		Angle Relationships		16:43
			Adjacent Angles	16:47
			Vertical Angles	17:49
			Linear Pair	19:40
		Angle Relationships		20:31
			Right Angles	20:32
			Supplementary Angles	21:15
			Complementary Angles	21:33
		Extra Example 1: Angles		24:08
		Extra Example 2: Angles		29:06
		Extra Example 3: Angles		32:05
		Extra Example 4 Angles		35:44
II. Reasoning & Proof
	Inductive Reasoning			19:00
		Intro		0:00
		Inductive Reasoning		0:05
			Conjecture	0:06
			Inductive Reasoning	0:15
		Examples		0:55
			Example: Sequence	0:56
			More Example: Sequence	2:00
		Using Inductive Reasoning		2:50
			Example: Conjecture	2:51
			More Example: Conjecture	3:48
		Counterexamples		4:56
			Counterexample	4:58
		Extra Example 1: Conjecture		6:59
		Extra Example 2: Sequence and Pattern		10:20
		Extra Example 3: Inductive Reasoning		12:46
		Extra Example 4: Conjecture and Counterexample		15:17
	Conditional Statements			42:47
		Intro		0:00
		If Then Statements		0:05
			If Then Statements	0:06
		Other Forms		2:29
			Example: Without Then	2:40
			Example: Using When	3:03
			Example: Hypothesis	3:24
		Identify the Hypothesis and Conclusion		3:52
			Example 1: Hypothesis and Conclusion	3:58
			Example 2: Hypothesis and Conclusion	4:31
			Example 3: Hypothesis and Conclusion	5:38
		Write in If Then Form		6:16
			Example 1: Write in If Then Form	6:23
			Example 2: Write in If Then Form	6:57
			Example 3: Write in If Then Form	7:39
		Other Statements		8:40
			Other Statements	8:41
		Converse Statements		9:18
			Converse Statements	9:20
		Converses and Counterexamples		11:04
			Converses and Counterexamples	11:05
			Example 1: Converses and Counterexamples	12:02
			Example 2: Converses and Counterexamples	15:10
			Example 3: Converses and Counterexamples	17:08
		Inverse Statement		19:58
			Definition and Example	19:59
		Inverse Statement		21:46
			Example 1: Inverse and Counterexample	21:47
			Example 2: Inverse and Counterexample	23:34
		Contrapositive Statement		25:20
			Definition and Example	25:21
		Contrapositive Statement		26:58
			Example: Contrapositive Statement	27:00
		Summary		29:03
			Summary of Lesson	29:04
		Extra Example 1: Hypothesis and Conclusion		32:20
		Extra Example 2: If-Then Form		33:23
		Extra Example 3: Converse, Inverse, and Contrapositive		34:54
		Extra Example 4: Converse, Inverse, and Contrapositive		37:56
	Point, Line, and Plane Postulates			17:24
		Intro		0:00
		What are Postulates?		0:09
			Definition of Postulates	0:10
		Postulates		1:22
			Postulate 1: Two Points	1:23
			Postulate 2: Three Points	2:02
			Postulate 3: Line	2:45
		Postulates, cont..		3:08
			Postulate 4: Plane	3:09
			Postulate 5: Two Points in a Plane	3:53
		Postulates, cont..		4:46
			Postulate 6: Two Lines Intersect	4:47
			Postulate 7: Two Plane Intersect	5:28
		Using the Postulates		6:34
			Examples: True or False	6:35
		Using the Postulates		10:18
			Examples: True or False	10:19
		Extra Example 1: Always, Sometimes, or Never		12:22
		Extra Example 2: Always, Sometimes, or Never		13:15
		Extra Example 3: Always, Sometimes, or Never		14:16
		Extra Example 4: Always, Sometimes, or Never		15:03
	Deductive Reasoning			36:03
		Intro		0:00
		Deductive Reasoning		0:06
			Definition of Deductive Reasoning	0:07
		Inductive vs. Deductive		2:51
			Inductive Reasoning	2:52
			Deductive reasoning	3:19
		Law of Detachment		3:47
			Law of Detachment	3:48
			Examples of Law of Detachment	4:31
		Law of Syllogism		7:32
			Law of Syllogism	7:33
			Example 1: Making a Conclusion	9:02
			Example 2: Making a Conclusion	12:54
		Using Laws of Logic		14:12
			Example 1: Determine the Logic	14:42
			Example 2: Determine the Logic	17:02
		Using Laws of Logic, cont.		18:47
			Example 3: Determine the Logic	19:03
			Example 4: Determine the Logic	20:56
		Extra Example 1: Determine the Conclusion and Law		22:12
		Extra Example 2: Determine the Conclusion and Law		25:39
		Extra Example 3: Determine the Logic and Law		29:50
		Extra Example 4: Determine the Logic and Law		31:27
	Proofs in Algebra: Properties of Equality			44:31
		Intro		0:00
		Properties of Equality		0:10
			Addition Property of Equality	0:28
			Subtraction Property of Equality	1:10
			Multiplication Property of Equality	1:41
			Division Property of Equality	1:55
			Addition Property of Equality Using Angles	2:46
		Properties of Equality, cont.		4:10
			Reflexive Property of Equality	4:11
			Symmetric Property of Equality	5:24
			Transitive Property of Equality	6:10
		Properties of Equality, cont.		7:04
			Substitution Property of Equality	7:05
			Distributive Property of Equality	8:34
		Two Column Proof		9:40
			Example: Two Column Proof	9:46
		Proof Example 1		16:13
		Proof Example 2		23:49
		Proof Example 3		30:33
		Extra Example 1: Name the Property of Equality		38:07
		Extra Example 2: Name the Property of Equality		40:16
		Extra Example 3: Name the Property of Equality		41:35
		Extra Example 4: Name the Property of Equality		43:02
	Proving Segment Relationship			41:02
		Intro		0:00
		Good Proofs		0:12
			Five Essential Parts	0:13
		Proof Reasons		1:38
			Undefined	1:40
			Definitions	2:06
			Postulates	2:42
			Previously Proven Theorems	3:24
		Congruence of Segments		4:10
			Theorem: Congruence of Segments	4:12
		Proof Example		10:16
			Proof: Congruence of Segments	10:17
		Setting Up Proofs		19:13
			Example: Two Segments with Equal Measures	19:15
		Setting Up Proofs		21:48
			Example: Vertical Angles are Congruent	21:50
		Setting Up Proofs		23:59
			Example: Segment of a Triangle	24:00
		Extra Example 1: Congruence of Segments		27:03
		Extra Example 2: Setting Up Proofs		28:50
		Extra Example 3: Setting Up Proofs		30:55
		Extra Example 4: Two-Column Proof		33:11
	Proving Angle Relationships			33:37
		Intro		0:00
		Supplement Theorem		0:05
			Supplementary Angles	0:06
		Congruence of Angles		2:37
			Proof: Congruence of Angles	2:38
		Angle Theorems		6:54
			Angle Theorem 1: Supplementary Angles	6:55
			Angle Theorem 2: Complementary Angles	10:25
		Angle Theorems		11:32
			Angle Theorem 3: Right Angles	11:35
			Angle Theorem 4: Vertical Angles	12:09
			Angle Theorem 5: Perpendicular Lines	12:57
		Using Angle Theorems		13:45
			Example 1: Always, Sometimes, or Never	13:50
			Example 2: Always, Sometimes, or Never	14:28
			Example 3: Always, Sometimes, or Never	16:21
		Extra Example 1: Always, Sometimes, or Never		16:53
		Extra Example 2: Find the Measure of Each Angle		18:55
		Extra Example 3: Find the Measure of Each Angle		25:03
		Extra Example 4: Two-Column Proof		27:08
III. Perpendicular & Parallel Lines
	Parallel Lines and Transversals			37:35
		Intro		0:00
		Lines		0:06
			Parallel Lines	0:09
			Skew Lines	2:02
			Transversal	3:42
		Angles Formed by a Transversal		4:28
			Interior Angles	5:53
			Exterior Angles	6:09
			Consecutive Interior Angles	7:04
			Alternate Exterior Angles	9:47
			Alternate Interior Angles	11:22
			Corresponding Angles	12:27
		Angles Formed by a Transversal		15:29
			Relationship Between Angles	15:30
		Extra Example 1: Intersecting, Parallel, or Skew		19:26
		Extra Example 2: Draw a Diagram		21:37
		Extra Example 3: Name the Figures		24:12
		Extra Example 4: Angles Formed by a Transversal		28:38
	Angles and Parallel Lines			41:53
		Intro		0:00
		Corresponding Angles Postulate		0:05
			Corresponding Angles Postulate	0:06
		Alternate Interior Angles Theorem		3:05
			Alternate Interior Angles Theorem	3:07
		Consecutive Interior Angles Theorem		5:16
			Consecutive Interior Angles Theorem	5:17
		Alternate Exterior Angles Theorem		6:42
			Alternate Exterior Angles Theorem	6:43
		Parallel Lines Cut by a Transversal		7:18
			Example: Parallel Lines Cut by a Transversal	7:19
		Perpendicular Transversal Theorem		14:54
			Perpendicular Transversal Theorem	14:55
		Extra Example 1: State the Postulate or Theorem		16:37
		Extra Example 2: Find the Measure of the Numbered Angle		18:53
		Extra Example 3: Find the Measure of Each Angle		25:13
		Extra Example 4: Find the Values of x, y, and z		36:26
	Slope of Lines			44:06
		Intro		0:00
		Definition of Slope		0:06
			Slope Equation	0:13
		Slope of a Line		3:45
			Example: Find the Slope of a Line	3:47
		Slope of a Line		8:38
			More Example: Find the Slope of a Line	8:40
		Slope Postulates		12:32
			Proving Slope Postulates	12:33
		Parallel or Perpendicular Lines		17:23
			Example: Parallel or Perpendicular Lines	17:24
		Using Slope Formula		20:02
			Example: Using Slope Formula	20:03
		Extra Example 1: Slope of a Line		25:10
		Extra Example 2: Slope of a Line		26:31
		Extra Example 3: Graph the Line		34:11
		Extra Example 4: Using the Slope Formula		38:50
	Proving Lines Parallel			25:55
		Intro		0:00
		Postulates		0:06
			Postulate 1: Parallel Lines	0:21
			Postulate 2: Parallel Lines	2:16
		Parallel Postulate		3:28
			Definition and Example of Parallel Postulate	3:29
		Theorems		4:29
			Theorem 1: Parallel Lines	4:40
			Theorem 2: Parallel Lines	5:37
		Theorems, cont.		6:10
			Theorem 3: Parallel Lines	6:11
		Extra Example 1: Determine Parallel Lines		6:56
		Extra Example 2: Find the Value of x		11:42
		Extra Example 3: Opposite Sides are Parallel		14:48
		Extra Example 4: Proving Parallel Lines		20:42
	Parallels and Distance			19:48
		Intro		0:00
		Distance Between a Points and Line		0:07
			Definition and Example	0:08
		Distance Between Parallel Lines		1:51
			Definition and Example	1:52
		Extra Example 1: Drawing a Segment to Represent Distance		3:02
		Extra Example 2: Drawing a Segment to Represent Distance		4:27
		Extra Example 3: Graph, Plot, and Construct a Perpendicular Segment		5:13
		Extra Example 4: Distance Between Two Parallel Lines		15:37
IV. Congruent Triangles
	Classifying Triangles			28:43
		Intro		0:00
		Triangles		0:09
			Triangle: A Three-Sided Polygon	0:10
			Sides	1:00
			Vertices	1:22
			Angles	1:56
		Classifying Triangles by Angles		2:59
			Acute Triangle	3:19
			Obtuse Triangle	4:08
			Right Triangle	4:44
		Equiangular Triangle		5:38
			Definition and Example of an Equiangular Triangle	5:39
		Classifying Triangles by Sides		6:57
			Scalene Triangle	7:17
			Isosceles Triangle	7:57
			Equilateral Triangle	8:12
		Isosceles Triangle		8:58
			Labeling Isosceles Triangle	9:00
			Labeling Right Triangle	10:44
		Isosceles Triangle		11:10
			Example: Find x, AB, BC, and AC	11:11
		Extra Example 1: Classify Each Triangle		13:45
		Extra Example 2: Always, Sometimes, or Never		16:28
		Extra Example 3: Find All the Sides of the Isosceles Triangle		20:29
		Extra Example 4: Distance Formula and Triangle		22:29
	Measuring Angles in Triangles			44:43
		Intro		0:00
		Angle Sum Theorem		0:09
			Angle Sum Theorem for Triangle	0:11
		Using Angle Sum Theorem		4:06
			Find the Measure of the Missing Angle	4:07
		Third Angle Theorem		4:58
			Example: Third Angle Theorem	4:59
		Exterior Angle Theorem		7:58
			Example: Exterior Angle Theorem	8:00
		Flow Proof of Exterior Angle Theorem		15:14
			Flow Proof of Exterior Angle Theorem	15:17
		Triangle Corollaries		27:21
			Triangle Corollary 1	27:50
			Triangle Corollary 2	30:42
		Extra Example 1: Find the Value of x		32:55
		Extra Example 2: Find the Value of x		34:20
		Extra Example 3: Find the Measure of the Angle		35:38
		Extra Example 4: Find the Measure of Each Numbered Angle		39:00
	Exploring Congruent Triangles			26:46
		Intro		0:00
		Congruent Triangles		0:15
			Example of Congruent Triangles	0:17
		Corresponding Parts		3:39
			Corresponding Angles and Sides of Triangles	3:40
		Definition of Congruent Triangles		11:24
			Definition of Congruent Triangles	11:25
		Triangle Congruence		16:37
			Congruence of Triangles	16:38
		Extra Example 1: Congruence Statement		18:24
		Extra Example 2: Congruence Statement		21:26
		Extra Example 3: Draw and Label the Figure		23:09
		Extra Example 4: Drawing Triangles		24:04
	Proving Triangles Congruent			47:51
		Intro		0:00
		SSS Postulate		0:18
			Side-Side-Side Postulate	0:27
		SAS Postulate		2:26
			Side-Angle-Side Postulate	2:29
		SAS Postulate		3:57
			Proof Example	3:58
		ASA Postulate		11:47
			Angle-Side-Angle Postulate	11:53
		AAS Theorem		14:13
			Angle-Angle-Side Theorem	14:14
		Methods Overview		16:16
			Methods Overview	16:17
			SSS	16:33
			SAS	17:06
			ASA	17:50
			AAS	18:17
			CPCTC	19:14
		Extra Example 1:Proving Triangles are Congruent		21:29
		Extra Example 2: Proof		25:40
		Extra Example 3: Proof		30:41
		Extra Example 4: Proof		38:41
	Isosceles and Equilateral Triangles			27:53
		Intro		0:00
		Isosceles Triangle Theorem		0:07
			Isosceles Triangle Theorem	0:09
		Isosceles Triangle Theorem		2:26
			Example: Using the Isosceles Triangle Theorem	2:27
		Isosceles Triangle Theorem Converse		3:29
			Isosceles Triangle Theorem Converse	3:30
		Equilateral Triangle Theorem Corollaries		4:30
			Equilateral Triangle Theorem Corollary 1	4:59
			Equilateral Triangle Theorem Corollary 2	5:55
		Extra Example 1: Find the Value of x		7:08
		Extra Example 2: Find the Value of x		10:04
		Extra Example 3: Proof		14:04
		Extra Example 4: Proof		22:41
V. Triangle Inequalities
	Special Segments in Triangles			43:44
		Intro		0:00
		Perpendicular Bisector		0:06
			Perpendicular Bisector	0:07
		Perpendicular Bisector		4:07
			Perpendicular Bisector Theorems	4:08
		Median		6:30
			Definition of Median	6:31
		Median		9:41
			Example: Median	9:42
		Altitude		12:22
			Definition of Altitude	12:23
		Angle Bisector		14:33
			Definition of Angle Bisector	14:34
		Angle Bisector		16:41
			Angle Bisector Theorems	16:42
		Special Segments Overview		18:57
			Perpendicular Bisector	19:04
			Median	19:32
			Altitude	19:49
			Angle Bisector	20:02
			Examples: Special Segments	20:18
		Extra Example 1: Draw and Label		22:36
		Extra Example 2: Draw the Altitudes for Each Triangle		24:37
		Extra Example 3: Perpendicular Bisector		27:57
		Extra Example 4: Draw, Label, and Write Proof		34:33
	Right Triangles			26:34
		Intro		0:00
		LL Theorem		0:21
			Leg-Leg Theorem	0:25
		HA Theorem		2:23
			Hypotenuse-Angle Theorem	2:24
		LA Theorem		4:49
			Leg-Angle Theorem	4:50
		LA Theorem		6:18
			Example: Find x and y	6:19
		HL Postulate		8:22
			Hypotenuse-Leg Postulate	8:23
		Extra Example 1: LA Theorem & HL Postulate		10:57
		Extra Example 2: Find x So That Each Pair of Triangles is Congruent		14:15
		Extra Example 3: Two-column Proof		17:02
		Extra Example 4: Two-column Proof		21:01
	Indirect Proofs and Inequalities			33:30
		Intro		0:00
		Writing an Indirect Proof		0:09
			Step 1	0:49
			Step 2	2:32
			Step 3	3:00
		Indirect Proof		4:30
			Example: 2 + 6 = 8	5:00
			Example: The Suspect is Guilty	5:40
			Example: Measure of Angle A < Measure of Angle B	6:06
		Definition of Inequality		7:47
			Definition of Inequality & Example	7:48
		Properties of Inequality		9:55
			Comparison Property	9:58
			Transitive Property	10:33
			Addition and Subtraction Properties	12:01
			Multiplication and Division Properties	13:07
		Exterior Angle Inequality Theorem		14:12
			Example: Exterior Angle Inequality Theorem	14:13
		Extra Example 1: Draw a Diagram for the Statement		18:32
		Extra Example 2: Name the Property for Each Statement		19:56
		Extra Example 3: State the Assumption		21:22
		Extra Example 4: Write an Indirect Proof		25:39
	Inequalities for Sides and Angles of a Triangle			17:26
		Intro		0:00
		Side to Angles		0:10
			If One Side of a Triangle is Longer Than Another Side	0:11
		Converse: Angles to Sides		1:57
			If One Angle of a Triangle Has a Greater Measure Than Another Angle	1:58
		Extra Example 1: Name the Angles in the Triangle From Least to Greatest		2:38
		Extra Example 2: Find the Longest and Shortest Segment in the Triangle		3:47
		Extra Example 3: Angles and Sides of a Triangle		4:51
		Extra Example 4: Two-column Proof		9:08
	Triangle Inequality			28:11
		Intro		0:00
		Triangle Inequality Theorem		0:05
			Triangle Inequality Theorem	0:06
		Triangle Inequality Theorem		4:22
			Example 1: Triangle Inequality Theorem	4:23
			Example 2: Triangle Inequality Theorem	9:40
		Extra Example 1: Determine if the Three Numbers can Represent the Sides of a Triangle		12:00
		Extra Example 2: Finding the Third Side of a Triangle		13:34
		Extra Example 3: Always True, Sometimes True, or Never True		18:18
		Extra Example 4: Triangle and Vertices		22:36
	Inequalities Involving Two Triangles			29:36
		Intro		0:00
		SAS Inequality Theorem		0:06
			SAS Inequality Theorem & Example	0:25
		SSS Inequality Theorem		4:33
			SSS Inequality Theorem & Example	4:34
		Extra Example 1: Write an Inequality Comparing the Segments		6:08
		Extra Example 2: Determine if the Statement is True		9:52
		Extra Example 3: Write an Inequality for x		14:20
		Extra Example 4: Two-column Proof		17:44
VI. Quadrilaterals
	Parallelograms			29:11
		Intro		0:00
		Quadrilaterals		0:06
			Four-sided Polygons	0:08
			Non Examples of Quadrilaterals	0:47
		Parallelograms		1:35
			Parallelograms	1:36
		Properties of Parallelograms		4:28
			Opposite Sides of a Parallelogram are Congruent	4:29
			Opposite Angles of a Parallelogram are Congruent	5:49
		Angles and Diagonals		6:24
			Consecutive Angles in a Parallelogram are Supplementary	6:25
			The Diagonals of a Parallelogram Bisect Each Other	8:42
		Extra Example 1: Complete Each Statement About the Parallelogram		10:26
		Extra Example 2: Find the Values of x, y, and z of the Parallelogram		13:21
		Extra Example 3: Find the Distance of Each Side to Verify the Parallelogram		16:35
		Extra Example 4: Slope of Parallelogram		23:15
	Proving Parallelograms			42:43
		Intro		0:00
		Parallelogram Theorems		0:09
			Theorem 1	0:20
			Theorem 2	1:50
		Parallelogram Theorems, Cont.		3:10
			Theorem 3	3:11
			Theorem 4	4:15
		Proving Parallelogram		6:21
			Example: Determine if Quadrilateral ABCD is a Parallelogram	6:22
		Summary		14:01
			Both Pairs of Opposite Sides are Parallel	14:14
			Both Pairs of Opposite Sides are Congruent	15:09
			Both Pairs of Opposite Angles are Congruent	15:24
			Diagonals Bisect Each Other	15:44
			A Pair of Opposite Sides is Both Parallel and Congruent	16:13
		Extra Example 1: Determine if Each Quadrilateral is a Parallelogram		16:54
		Extra Example 2: Find the Value of x and y		20:23
		Extra Example 3: Determine if the Quadrilateral ABCD is a Parallelogram		24:05
		Extra Example 4: Two-column Proof		30:28
	Rectangles			29:47
		Intro		0:00
		Rectangles		0:03
			Definition of Rectangles	0:04
		Diagonals of Rectangles		2:52
			Rectangles: Diagonals Property 1	2:53
			Rectangles: Diagonals Property 2	3:30
		Proving a Rectangle		4:40
			Example: Determine Whether Parallelogram ABCD is a Rectangle	4:41
		Rectangles Summary		9:22
			Opposite Sides are Congruent and Parallel	9:40
			Opposite Angles are Congruent	9:51
			Consecutive Angles are Supplementary	9:58
			Diagonals are Congruent and Bisect Each Other	10:05
			All Four Angles are Right Angles	10:40
		Extra Example 1: Find the Value of x		11:03
		Extra Example 2: Name All Congruent Sides and Angles		13:52
		Extra Example 3: Always, Sometimes, or Never True		19:39
		Extra Example 4: Determine if ABCD is a Rectangle		26:45
	Squares and Rhombi			39:14
		Intro		0:00
		Rhombus		0:09
			Definition of a Rhombus	0:10
		Diagonals of a Rhombus		2:03
			Rhombus: Diagonals Property 1	2:21
			Rhombus: Diagonals Property 2	3:49
			Rhombus: Diagonals Property 3	4:36
		Rhombus		6:17
			Example: Use the Rhombus to Find the Missing Value	6:18
		Square		8:17
			Definition of a Square	8:20
		Summary Chart		11:06
			Parallelogram	11:07
			Rectangle	12:56
			Rhombus	13:54
			Square	14:44
		Extra Example 1: Diagonal Property		15:44
		Extra Example 2: Use Rhombus ABCD to Find the Missing Value		19:39
		Extra Example 3: Always, Sometimes, or Never True		23:06
		Extra Example 4: Determine the Quadrilateral		28:02
	Trapezoids and Kites			30:48
		Intro		0:00
		Trapezoid		0:10
			Definition of Trapezoid	0:12
		Isosceles Trapezoid		2:57
			Base Angles of an Isosceles Trapezoid	2:58
			Diagonals of an Isosceles Trapezoid	4:05
		Median of a Trapezoid		4:26
			Median of a Trapezoid	4:27
		Median of a Trapezoid		6:41
			Median Formula	7:00
		Kite		8:28
			Definition of a Kite	8:29
		Quadrilaterals Summary		11:19
			A Quadrilateral with Two Pairs of Adjacent Congruent Sides	11:20
		Extra Example 1: Isosceles Trapezoid		14:50
		Extra Example 2: Median of Trapezoid		18:28
		Extra Example 3: Always, Sometimes, or Never		24:13
		Extra Example 4: Determine if the Figure is a Trapezoid		26:49
VII. Proportions and Similarity
	Using Proportions and Ratios			20:10
		Intro		0:00
		Ratio		0:05
			Definition and Examples of Writing Ratio	0:06
		Proportion		2:05
			Definition of Proportion	2:06
			Examples of Proportion	2:29
		Using Ratio		5:53
			Example: Ratio	5:54
		Extra Example 1: Find Three Ratios Equivalent to 2/5		9:28
		Extra Example 2: Proportion and Cross Products		10:32
		Extra Example 3: Express Each Ratio as a Fraction		13:18
		Extra Example 4: Fin the Measure of a 3:4:5 Triangle		17:26
	Similar Polygons			27:53
		Intro		0:00
		Similar Polygons		0:05
			Definition of Similar Polygons	0:06
			Example of Similar Polygons	2:32
		Scale Factor		4:26
			Scale Factor: Definition and Example	4:27
		Extra Example 1: Determine if Each Pair of Figures is Similar		7:03
		Extra Example 2: Find the Values of x and y		11:33
		Extra Example 3: Similar Triangles		19:57
		Extra Example 4: Draw Two Similar Figures		23:36
	Similar Triangles			34:10
		Intro		0:00
		AA Similarity		0:10
			Definition of AA Similarity	0:20
			Example of AA Similarity	2:32
		SSS Similarity		4:46
			Definition of SSS Similarity	4:47
			Example of SSS Similarity	6:00
		SAS Similarity		8:04
			Definition of SAS Similarity	8:05
			Example of SAS Similarity	9:12
		Extra Example 1: Determine Whether Each Pair of Triangles is Similar		10:59
		Extra Example 2: Determine Which Triangles are Similar		16:08
		Extra Example 3: Determine if the Statement is True or False		23:11
		Extra Example 4: Write Two-Column Proof		26:25
	Parallel Lines and Proportional Parts			24:07
		Intro		0:00
		Triangle Proportionality		0:07
			Definition of Triangle Proportionality	0:08
			Example of Triangle Proportionality	0:51
		Triangle Proportionality Converse		2:19
			Triangle Proportionality Converse	2:20
		Triangle Mid-segment		3:42
			Triangle Mid-segment: Definition and Example	3:43
		Parallel Lines and Transversal		6:51
			Parallel Lines and Transversal	6:52
		Extra Example 1: Complete Each Statement		8:59
		Extra Example 2: Determine if the Statement is True or False		12:28
		Extra Example 3: Find the Value of x and y		15:35
		Extra Example 4: Find Midpoints of a Triangle		20:43
	Parts of Similar Triangles			27:06
		Intro		0:00
		Proportional Perimeters		0:09
			Proportional Perimeters: Definition and Example	0:10
		Similar Altitudes		2:23
			Similar Altitudes: Definition and Example	2:24
		Similar Angle Bisectors		4:50
			Similar Angle Bisectors: Definition and Example	4:51
		Similar Medians		6:05
			Similar Medians: Definition and Example	6:06
		Angle Bisector Theorem		7:33
			Angle Bisector Theorem	7:34
		Extra Example 1: Parts of Similar Triangles		10:52
		Extra Example 2: Parts of Similar Triangles		14:57
		Extra Example 3: Parts of Similar Triangles		19:27
		Extra Example 4: Find the Perimeter of Triangle ABC		23:14
VIII. Applying Right Triangles & Trigonometry
	Pythagorean Theorem			21:14
		Intro		0:00
		Pythagorean Theorem		0:05
			Pythagorean Theorem & Example	0:06
		Pythagorean Converse		1:20
			Pythagorean Converse & Example	1:21
		Pythagorean Triple		2:42
			Pythagorean Triple	2:43
		Extra Example 1: Find the Missing Side		4:59
		Extra Example 2: Determine Right Triangle		7:40
		Extra Example 3: Determine Pythagorean Triple		11:30
		Extra Example 4: Vertices and Right Triangle		14:29
	Geometric Mean			40:59
		Intro		0:00
		Geometric Mean		0:04
			Geometric Mean & Example	0:05
		Similar Triangles		4:32
			Similar Triangles	4:33
		Geometric Mean-Altitude		11:10
			Geometric Mean-Altitude & Example	11:11
		Geometric Mean-Leg		14:47
			Geometric Mean-Leg & Example	14:18
		Extra Example 1: Geometric Mean Between Each Pair of Numbers		20:10
		Extra Example 2: Similar Triangles		23:46
		Extra Example 3: Geometric Mean of Triangles		28:30
		Extra Example 4: Geometric Mean of Triangles		36:58
	Special Right Triangles			37:57
		Intro		0:00
		45-45-90 Triangles		0:06
			Definition of 45-45-90 Triangles	0:25
		45-45-90 Triangles		5:51
			Example: Find n	5:52
		30-60-90 Triangles		8:59
			Definition of 30-60-90 Triangles	9:00
		30-60-90 Triangles		12:25
			Example: Find n	12:26
		Extra Example 1: Special Right Triangles		15:08
		Extra Example 2: Special Right Triangles		18:22
		Extra Example 3: Word Problems & Special Triangles		27:40
		Extra Example 4: Hexagon & Special Triangles		33:51
	Ratios in Right Triangles			40:37
		Intro		0:00
		Trigonometric Ratios		0:08
			Definition of Trigonometry	0:13
			Sine (sin), Cosine (cos), & Tangent (tan)	0:50
		Trigonometric Ratios		3:04
			Trig Functions	3:05
			Inverse Trig Functions	5:02
		SOHCAHTOA		8:16
			sin x	9:07
			cos x	10:00
			tan x	10:32
			Example: SOHCAHTOA & Triangle	12:10
		Extra Example 1: Find the Value of Each Ratio or Angle Measure		14:36
		Extra Example 2: Find Sin, Cos, and Tan		18:51
		Extra Example 3: Find the Value of x Using SOHCAHTOA		22:55
		Extra Example 4: Trigonometric Ratios in Right Triangles		32:13
	Angles of Elevation and Depression			21:04
		Intro		0:00
		Angle of Elevation		0:10
			Definition of Angle of Elevation & Example	0:11
		Angle of Depression		1:19
			Definition of Angle of Depression & Example	1:20
		Extra Example 1: Name the Angle of Elevation and Depression		2:22
		Extra Example 2: Word Problem & Angle of Depression		4:41
		Extra Example 3: Word Problem & Angle of Elevation		14:02
		Extra Example 4: Find the Missing Measure		18:10
	Law of Sines			35:25
		Intro		0:00
		Law of Sines		0:20
			Law of Sines	0:21
		Law of Sines		3:34
			Example: Find b	3:35
		Solving the Triangle		9:19
			Example: Using the Law of Sines to Solve Triangle	9:20
		Extra Example 1: Law of Sines and Triangle		17:43
		Extra Example 2: Law of Sines and Triangle		20:06
		Extra Example 3: Law of Sines and Triangle		23:54
		Extra Example 4: Law of Sines and Triangle		28:59
	Law of Cosines			52:43
		Intro		0:00
		Law of Cosines		0:35
			Law of Cosines	0:36
		Law of Cosines		6:22
			Use the Law of Cosines When Both are True	6:23
		Law of Cosines		8:35
			Example: Law of Cosines	8:36
		Extra Example 1: Law of Sines or Law of Cosines?		13:35
		Extra Example 2: Use the Law of Cosines to Find the Missing Measure		17:02
		Extra Example 3: Solve the Triangle		30:49
		Extra Example 4: Find the Measure of Each Diagonal of the Parallelogram		41:39
IX. Circles
	Segments in a Circle			22:43
		Intro		0:00
		Segments in a Circle		0:10
			Circle	0:11
			Chord	0:59
			Diameter	1:32
			Radius	2:07
			Secant	2:17
			Tangent	3:10
		Circumference		3:56
			Introduction to Circumference	3:57
			Example: Find the Circumference of the Circle	5:09
		Circumference		6:40
			Example: Find the Circumference of the Circle	6:41
		Extra Example 1: Use the Circle to Answer the Following		9:10
		Extra Example 2: Find the Missing Measure		12:53
		Extra Example 3: Given the Circumference, Find the Perimeter of the Triangle		15:51
		Extra Example 4: Find the Circumference of Each Circle		19:24
	Angles and Arc			35:24
		Intro		0:00
		Central Angle		0:06
			Definition of Central Angle	0:07
		Sum of Central Angles		1:17
			Sum of Central Angles	1:18
		Arcs		2:27
			Minor Arc	2:30
			Major Arc	3:47
		Arc Measure		5:24
			Measure of Minor Arc	5:24
			Measure of Major Arc	6:53
			Measure of a Semicircle	7:11
		Arc Addition Postulate		8:25
			Arc Addition Postulate	8:26
		Arc Length		9:43
			Arc Length and Example	9:44
		Concentric Circles		16:05
			Concentric Circles	16:06
		Congruent Circles and Arcs		17:50
			Congruent Circles	17:51
			Congruent Arcs	18:47
		Extra Example 1: Minor Arc, Major Arc, and Semicircle		20:14
		Extra Example 2: Measure and Length of Arc		22:52
		Extra Example 3: Congruent Arcs		25:48
		Extra Example 4: Angles and Arcs		30:33
	Arcs and Chords			21:51
		Intro		0:00
		Arcs and Chords		0:07
			Arc of the Chord	0:08
			Theorem 1: Congruent Minor Arcs	1:01
		Inscribed Polygon		2:10
			Inscribed Polygon	2:11
		Arcs and Chords		3:18
			Theorem 2: When a Diameter is Perpendicular to a Chord	3:19
		Arcs and Chords		5:05
			Theorem 3: Congruent Chords	5:06
		Extra Example 1: Congruent Arcs		10:35
		Extra Example 2: Length of Arc		13:50
		Extra Example 3: Arcs and Chords		17:09
		Extra Example 4: Arcs and Chords		19:45
	Inscribed Angles			27:53
		Intro		0:00
		Inscribed Angles		0:07
			Definition of Inscribed Angles	0:08
		Inscribed Angles		0:58
			Inscribed Angle Theorem 1	0:59
		Inscribed Angles		3:29
			Inscribed Angle Theorem 2	3:30
		Inscribed Angles		4:38
			Inscribed Angle Theorem 3	4:39
		Inscribed Quadrilateral		5:50
			Inscribed Quadrilateral	5:51
		Extra Example 1: Central Angle, Inscribed Angle, and Intercepted Arc		7:02
		Extra Example 2: Inscribed Angles		9:24
		Extra Example 3: Inscribed Angles		14:00
		Extra Example 4: Complete the Proof		17:58
	Tangents			26:16
		Intro		0:00
		Tangent Theorems		0:04
			Tangent Theorem 1	0:05
			Tangent Theorem 1 Converse	0:55
		Common Tangents		1:34
			Common External Tangent	2:12
			Common Internal Tangent	2:30
		Tangent Segments		3:08
			Tangent Segments	3:09
		Circumscribed Polygons		4:11
			Circumscribed Polygons	4:12
		Extra Example 1: Tangents & Circumscribed Polygons		5:50
		Extra Example 2: Tangents & Circumscribed Polygons		8:35
		Extra Example 3: Tangents & Circumscribed Polygons		11:50
		Extra Example 4: Tangents & Circumscribed Polygons		15:43
	Secants, Tangents, & Angle Measures			27:50
		Intro		0:00
		Secant		0:08
			Secant	0:09
		Secant and Tangent		0:49
			Secant and Tangent	0:50
		Interior Angles		2:56
			Secants & Interior Angles	2:57
		Exterior Angles		7:21
			Secants & Exterior Angles	7:22
		Extra Example 1: Secants, Tangents, & Angle Measures		10:53
		Extra Example 2: Secants, Tangents, & Angle Measures		13:31
		Extra Example 3: Secants, Tangents, & Angle Measures		19:54
		Extra Example 4: Secants, Tangents, & Angle Measures		22:29
	Special Segments in a Circle			23:08
		Intro		0:00
		Chord Segments		0:05
			Chord Segments	0:06
		Secant Segments		1:36
			Secant Segments	1:37
		Tangent and Secant Segments		4:10
			Tangent and Secant Segments	4:11
		Extra Example 1: Special Segments in a Circle		5:53
		Extra Example 2: Special Segments in a Circle		7:58
		Extra Example 3: Special Segments in a Circle		11:24
		Extra Example 4: Special Segments in a Circle		18:09
	Equations of Circles			27:01
		Intro		0:00
		Equation of a Circle		0:06
			Standard Equation of a Circle	0:07
			Example 1: Equation of a Circle	0:57
			Example 2: Equation of a Circle	1:36
		Extra Example 1: Determine the Coordinates of the Center and the Radius		4:56
		Extra Example 2: Write an Equation Based on the Given Information		7:53
		Extra Example 3: Graph Each Circle		16:48
		Extra Example 4: Write the Equation of Each Circle		19:17
X. Polygons & Area
	Polygons			27:24
		Intro		0:00
		Polygons		0:10
			Polygon vs. Not Polygon	0:18
		Convex and Concave		1:46
			Convex vs. Concave Polygon	1:52
		Regular Polygon		4:04
			Regular Polygon	4:05
		Interior Angle Sum Theorem		4:53
			Triangle	5:03
			Quadrilateral	6:05
			Pentagon	6:38
			Hexagon	7:59
			20-Gon	9:36
		Exterior Angle Sum Theorem		12:04
			Exterior Angle Sum Theorem	12:05
		Extra Example 1: Drawing Polygons		13:51
		Extra Example 2: Convex Polygon		15:16
		Extra Example 3: Exterior Angle Sum Theorem		18:21
		Extra Example 4: Interior Angle Sum Theorem		22:20
	Area of Parallelograms			17:46
		Intro		0:00
		Parallelograms		0:06
			Definition and Area Formula	0:07
		Area of Figure		2:00
			Area of Figure	2:01
		Extra Example 1:Find the Area of the Shaded Area		3:14
		Extra Example 2: Find the Height and Area of the Parallelogram		6:00
		Extra Example 3: Find the Area of the Parallelogram Given Coordinates and Vertices		10:11
		Extra Example 4: Find the Area of the Figure		14:31
	Area of Triangles Rhombi, & Trapezoids			20:31
		Intro		0:00
		Area of a Triangle		0:06
			Area of a Triangle: Formula and Example	0:07
		Area of a Trapezoid		2:31
			Area of a Trapezoid: Formula	2:32
			Area of a Trapezoid: Example	6:55
		Area of a Rhombus		8:05
			Area of a Rhombus: Formula and Example	8:06
		Extra Example 1: Find the Area of the Polygon		9:51
		Extra Example 2: Find the Area of the Figure		11:19
		Extra Example 3: Find the Area of the Figure		14:16
		Extra Example 4: Find the Height of the Trapezoid		18:10
	Area of Regular Polygons & Circles			36:43
		Intro		0:00
		Regular Polygon		0:08
			SOHCAHTOA	0:54
			30-60-90 Triangle	1:52
			45-45-90 Triangle	2:40
		Area of a Regular Polygon		3:39
			Area of a Regular Polygon	3:40
		Are of a Circle		7:55
			Are of a Circle	7:56
		Extra Example 1: Find the Area of the Regular Polygon		8:22
		Extra Example 2: Find the Area of the Regular Polygon		16:48
		Extra Example 3: Find the Area of the Shaded Region		24:11
		Extra Example 4: Find the Area of the Shaded Region		32:24
	Perimeter & Area of Similar Figures			18:17
		Intro		0:00
		Perimeter of Similar Figures		0:08
			Example: Scale Factor & Perimeter of Similar Figures	0:09
		Area of Similar Figures		2:44
			Example:Scale Factor & Area of Similar Figures	2:55
		Extra Example 1: Complete the Table		6:09
		Extra Example 2: Find the Ratios of the Perimeter and Area of the Similar Figures		8:56
		Extra Example 3: Find the Unknown Area		12:04
		Extra Example 4: Use the Given Area to Find AB		14:26
	Geometric Probability			38:40
		Intro		0:00
		Length Probability Postulate		0:05
			Length Probability Postulate	0:06
		Are Probability Postulate		2:34
			Are Probability Postulate	2:35
		Are of a Sector of a Circle		4:11
			Are of a Sector of a Circle Formula	4:12
			Are of a Sector of a Circle Example	7:51
		Extra Example 1: Length Probability		11:07
		Extra Example 2: Area Probability		12:14
		Extra Example 3: Area Probability		17:17
		Extra Example 4: Area of a Sector of a Circle		26:23
XI. Solids
	Three-Dimensional Figures			23:39
		Intro		0:00
		Polyhedrons		0:05
			Polyhedrons: Definition and Examples	0:06
			Faces	1:08
			Edges	1:55
			Vertices	2:23
		Solids		2:51
			Pyramid	2:54
			Cylinder	3:45
			Cone	4:09
			Sphere	4:23
		Prisms		5:00
			Rectangular, Regular, and Cube Prisms	5:02
		Platonic Solids		9:48
			Five Types of Regular Polyhedra	9:49
		Slices and Cross Sections		12:07
			Slices	12:08
			Cross Sections	12:47
		Extra Example 1: Name the Edges, Faces, and Vertices of the Polyhedron		14:23
		Extra Example 2: Determine if the Figure is a Polyhedron and Explain Why		17:37
		Extra Example 3: Describe the Slice Resulting from the Cut		19:12
		Extra Example 4: Describe the Shape of the Intersection		21:25
	Surface Area of Prisms and Cylinders			38:50
		Intro		0:00
		Prisms		0:06
			Bases	0:07
			Lateral Faces	0:52
			Lateral Edges	1:19
			Altitude	1:58
		Prisms		2:24
			Right Prism	2:25
			Oblique Prism	2:56
		Classifying Prisms		3:27
			Right Rectangular Prism	3:28
				4:55
			Oblique Pentagonal Prism	6:26
			Right Hexagonal Prism	7:14
		Lateral Area of a Prism		7:42
			Lateral Area of a Prism	7:43
		Surface Area of a Prism		13:44
			Surface Area of a Prism	13:45
		Cylinder		16:18
			Cylinder: Right and Oblique	16:19
		Lateral Area of a Cylinder		18:02
			Lateral Area of a Cylinder	18:03
		Surface Area of a Cylinder		20:54
			Surface Area of a Cylinder	20:55
		Extra Example 1: Find the Lateral Area and Surface Are of the Prism		21:51
		Extra Example 2: Find the Lateral Area of the Prism		28:15
		Extra Example 3: Find the Surface Area of the Prism		31:57
		Extra Example 4: Find the Lateral Area and Surface Area of the Cylinder		34:17
	Surface Area of Pyramids and Cones			26:10
		Intro		0:00
		Pyramids		0:07
			Pyramids	0:08
		Regular Pyramids		1:52
			Regular Pyramids	1:53
		Lateral Area of a Pyramid		4:33
			Lateral Area of a Pyramid	4:34
		Surface Area of a Pyramid		9:19
			Surface Area of a Pyramid	9:20
		Cone		10:09
			Right and Oblique Cone	10:10
		Lateral Area and Surface Area of a Right Cone		11:20
			Lateral Area and Surface Are of a Right Cone	11:21
		Extra Example 1: Pyramid and Prism		13:11
		Extra Example 2: Find the Lateral Area of the Regular Pyramid		15:00
		Extra Example 3: Find the Surface Area of the Pyramid		18:29
		Extra Example 4: Find the Lateral Area and Surface Area of the Cone		22:08
	Volume of Prisms and Cylinders			21:59
		Intro		0:00
		Volume of Prism		0:08
			Volume of Prism	0:10
		Volume of Cylinder		3:38
			Volume of Cylinder	3:39
		Extra Example 1: Find the Volume of the Prism		5:10
		Extra Example 2: Find the Volume of the Cylinder		8:03
		Extra Example 3: Find the Volume of the Prism		9:35
		Extra Example 4: Find the Volume of the Solid		19:06
	Volume of Pyramids and Cones			22:02
		Intro		0:00
		Volume of a Cone		0:08
			Volume of a Cone: Example	0:10
		Volume of a Pyramid		3:02
			Volume of a Pyramid: Example	3:03
		Extra Example 1: Find the Volume of the Pyramid		4:56
		Extra Example 2: Find the Volume of the Solid		6:01
		Extra Example 3: Find the Volume of the Pyramid		10:28
		Extra Example 4: Find the Volume of the Octahedron		16:23
	Surface Area and Volume of Spheres			14:46
		Intro		0:00
		Special Segments		0:06
			Radius	0:07
			Chord	0:31
			Diameter	0:55
			Tangent	1:20
		Sphere		1:43
			Plane & Sphere	1:44
			Hemisphere	2:56
		Surface Area of a Sphere		3:25
			Surface Area of a Sphere	3:26
		Volume of a Sphere		4:08
			Volume of a Sphere	4:09
		Extra Example 1: Determine Whether Each Statement is True or False		4:24
		Extra Example 2: Find the Surface Area of the Sphere		6:17
		Extra Example 3: Find the Volume of the Sphere with a Diameter of 20 Meters		7:25
		Extra Example 4: Find the Surface Area and Volume of the Solid		9:17
	Congruent and Similar Solids			16:06
		Intro		0:00
		Scale Factor		0:06
			Scale Factor: Definition and Example	0:08
		Congruent Solids		1:09
			Congruent Solids	1:10
		Similar Solids		2:17
			Similar Solids	2:18
		Extra Example 1: Determine if Each Pair of Solids is Similar, Congruent, or Neither		3:35
		Extra Example 2: Determine if Each Statement is True or False		7:47
		Extra Example 3: Find the Scale Factor and the Ratio of the Surface Areas and Volume		10:14
		Extra Example 4: Find the Volume of the Larger Prism		12:14
XII. Transformational Geometry
	Mapping			14:12
		Intro		0:00
		Transformation		0:04
			Rotation	0:32
			Translation	1:03
			Reflection	1:17
			Dilation	1:24
		Transformations		1:45
			Examples	1:46
		Congruence Transformation		2:51
			Congruence Transformation	2:52
		Extra Example 1: Describe the Transformation that Occurred in the Mappings		3:37
		Extra Example 2: Determine if the Transformation is an Isometry		5:16
		Extra Example 3: Isometry		8:16
	Reflections			23:17
		Intro		0:00
		Reflection		0:05
			Definition of Reflection	0:06
			Line of Reflection	0:35
			Point of Reflection	1:22
		Symmetry		1:59
			Line of Symmetry	2:00
			Point of Symmetry	2:48
		Extra Example 1: Draw the Image over the Line of Reflection and the Point of Reflection		3:45
		Extra Example 2: Determine Lines and Point of Symmetry		6:59
		Extra Example 3: Graph the Reflection of the Polygon		11:15
		Extra Example 4: Graph the Coordinates		16:07
	Translations			18:43
		Intro		0:00
		Translation		0:05
			Translation: Preimage & Image	0:06
			Example	0:56
		Composite of Reflections		6:28
			Composite of Reflections	6:29
		Extra Example 1: Translation		7:48
		Extra Example 2: Image, Preimage, and Translation		12:38
		Extra Example 3: Find the Translation Image Using a Composite of Reflections		15:08
		Extra Example 4: Find the Value of Each Variable in the Translation		17:18
	Rotations			21:26
		Intro		0:00
		Rotations		0:04
			Rotations	0:05
		Performing Rotations		2:13
			Composite of Two Successive Reflections over Two Intersecting Lines	2:14
			Angle of Rotation: Angle Formed by Intersecting Lines	4:29
		Angle of Rotation		5:30
			Rotation Postulate	5:31
		Extra Example 1: Find the Rotated Image		7:32
		Extra Example 2: Rotations and Coordinate Plane		10:33
		Extra Example 3: Find the Value of Each Variable in the Rotation		14:29
		Extra Example 4: Draw the Polygon Rotated 90 Degree Clockwise about P		16:13
	Dilation			37:06
		Intro		0:00
		Dilations		0:06
			Dilations	0:07
		Scale Factor		1:36
			Scale Factor	1:37
			Example 1	2:06
			Example 2	6:22
		Scale Factor		8:20
			Positive Scale Factor	8:21
			Negative Scale Factor	9:25
			Enlargement	12:43
			Reduction	13:52
		Extra Example 1: Find the Scale Factor		16:39
		Extra Example 2: Find the Measure of the Dilation Image		19:32
		Extra Example 3: Find the Coordinates of the Image with Scale Factor and the Origin as the Center of Dilation		26:18
		Extra Example 4: Graphing Polygon, Dilation, and Scale Factor		32:08

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Indirect Proofs and Inequalities

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Indirect Proofs and Inequalities

Indirect Proofs and Inequalities

Mathematics: Geometry

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