1. 7-4 Applying Properties of Similar Triangles
Geometry

2. 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

3. 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

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

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

6. 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

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

8. 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

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

10. Assignment

11. Example 4 N M L K
Extra Ex. 4