4.3 Warm Up Are the triangles similar? If so, which theorem justifies your answer.

4.3 Theorems about Proportions SWBAT use the Triangle Proportionality theorem and the Triangle Mid-segment theorem to solve for missing sides of triangles.

Angle Bisector and Proportional Side Theorem When an interior angle of a triangle is bisected, 2 similar triangles are formed. A bisector of an angle in a triangle divides the opposite side into 2 segments whose lengths are the same ratio as the length of the adjacent to the angle If AB = BD AC DC Then

24 = 8 30 DB 24DB = 240 24DB = 240 24 24 DB = 10

If DE II BC, Then AD = AE DB EC

Example

If L1 II L2 II L3, Then AB = DE BC EF

Example

If the midsegment JG is parallel to DS, then JG = DS 2 5 10 If the midsegment JG is parallel to DS, then JG = DS 2