Geometry Rectangles

Rectangles

Determine whether the following statement is true or false.
If a quadrilateral is a rectangle, then it is also a parallelogram.

True.

Write all the congruent segments in rectangle ABCD.

―AB ≅ ―CD , ―AD ≅ ―BC , ―AC ≅ ―BD , ―AE ≅ ―CE , ―AE ≅ ―BE , ―AE ≅ ―DE , ―BE ≅ ―CE , ―BE ≅ ―DE ,―CE ≅ ―DE .

Write all the right angles in rectangle ABCD.

∠ABC, ∠BCD, ∠CDA, ∠DAB.

Determine whether the following statement is true or false.
If ―AC ≅ ―BD and ―AC bisect ―BD at E, then quadrilateral ABCD is a rectangle.

True.

Determine whether the following statement is true or false.

If quadrilateral ABCD is a rectangle, then ∆ ABC ≅ ∆ DCB.

True.

m∠CAD = 30^o, find m ACD.

• m∠CAD + m∠ACD + m∠ADC = 180^o
• m∠ACD = 180^o − m∠CAD − m∠ADC
• m∠ACD = 180^o − 30^o − 90^o

m∠ACD = 60^o.

Determine whether each statement is always, sometimes, or never true.
If the oppsite sides of a quadrilateral are congruent and parallel, then the quadrilatetral is a rectangle.

Sometimes.

BE = 3x + 9, AE = 2x + 6, find x.

• ―BE ≅ ―AE
• 3x + 9 = 2x + 6

x = − 3.

AB = 4x + 5, CD = 17, find x.

• ―AB ≅ ―CD
• 4x + 5 = 17

x = 3.

Determine whether quadrilateral is a rectangle or not.

• A( − 2, 1), B( − 1, − 3), C(3, − 2), D(2, 2)
• the slope is m_AB = [( − 3 − 1)/( − 1 − ( − 2))] = − 4
• m_CD = [(2 − ( − 2))/(2 − 3)] = − 4
• m_AD = [(2 − 1)/(2 − ( − 2))] = [1/4]
• m_BC = [( − 2 − ( − 3))/(3 − ( − 1))] = [1/4]
• m_AB = m_CD, m_AD = m_BC
• Quadrilateral ABCD is a parallelogram.
• AC = √{(3 − ( − 2))² + ( − 2 − 1)²} = √{25 + 9} = √{34}
• BD = √{(2 − ( − 1))² + (2 − ( − 3))²} = √{9 + 25} = √{34}
• AC = BD
• ―AC ≅ ―BD

Parallelogram ABCD is a rectangle.

Rectangles

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.

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• Intro 0:00
• Rectangles 0:03
• Definition of Rectangles
• Diagonals of Rectangles 2:52
• Rectangles: Diagonals Property 1
• Rectangles: Diagonals Property 2
• Proving a Rectangle 4:40
• Example: Determine Whether Parallelogram ABCD is a Rectangle
• Rectangles Summary 9:22
• Opposite Sides are Congruent and Parallel
• Opposite Angles are Congruent
• Consecutive Angles are Supplementary
• Diagonals are Congruent and Bisect Each Other
• All Four Angles are Right Angles
• 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