7-4 Applying Properties of Similar Triangles Geometry

Theorem 7-4-1 Triangle Proportionality Theorem If a line parallel to a side of a triangle intersects the other two sides, then it divides the two sides proportionally. A E F B C

Theorem 7-4-2 Converse of the Triangle Proportionality Theorem If a line divides two sides of a triangle proportionally, then it is parallel to the third side. A E F B C

Example 1 In the diagram, U V Y X W Extra Ex. 1

Example 2 Verify that 15 10 B D A 8 E 12 C Extra Ex. 2

Theorem 7-4-3 Two Transversal Proportionality If three or more parallel lines intersect two transversals, then they divide the transversals proportionally. A B r s C D t E F l m

Example 3 In the diagram, C B A F D E 3 2 1 Extra Example 3

Theorem 7-4-4 Triangle Angle Bisector Theorem An angle bisector of a triangle divides the opposite side into 2 segments whose lengths are proportional to the lengths of the other two sides. C B A D

Ex. 4 Find PS & SR P S x+5 Q R 40 X-2 32

Assignment

Example 4 N M L K Extra Ex. 4