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### Parallel Lines and Proportional Parts

• If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments
• Triangle Proportionality Converse: If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side
• Triangle Mid-segment: A segment whose endpoints are the midpoints of two sides of a triangle is parallel to the third side of the triangle, and its length is one-half the length of the third side
• If three or more parallel lines intersect two transversals, then they cut off the transversals proportionally
• If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments one very transversal

## Parallel Lines and Proportional Parts

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