Warm-Up 1 In the diagram, DE is parallel to AC. Name a pair of similar triangles and explain why they are similar.

Warm-Up 2

Warm-Up 3

6.6: Use Proportionality Theorems Objectives: 1.To discover, present, and use various theorems involving proportions with parallel lines and triangles

Mini-Investigations In this lesson, each group will be responsible for investigating a particular proportionality theorem, solving some problems with their new theorem, and then presenting their results to the rest of the class.

Proportionality Theorems! Triangle Proportionality Theorem If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

Proportionality Theorems! Converse of the Triangle Proportionality Theorem If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Proportionality Theorems! If three parallel lines intersect two transversals, then they divide the transversals proportionally.

Proportionality Theorems! Angle Bisector Proportionality Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the other two sides.