1. Applying Properties of Similar Triangles
Sections 7-4 & 7-5

2. Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides the sides proportionally. B D E
Add parallel markings on bases A C

3. Converse of Triangle Proportionality Theorem
If a line divides the sides of a triangle proportionally, then it is parallel to the third side. B D E
Add parallel markings on bases A C

4. Corollary: Two-Transversal Proportionality
If three or more parallel lines
intersect two transversals, then
they divide transversals proportionally. A B C D E F
Add parallel markings on bases

5. Triangle Angle Bisector Theorem A triangle’s angle bisector
divides the opposite side into 2 segments
whose lengths are proportional to the lengths of the other 2 sides. A
Add parallel markings on bases B C D

6. Triangle Angle Bisector Theorem A triangle’s angle bisector
divides the opposite side into 2 segments
whose lengths are proportional to the lengths of the other 2 sides. A 4 6
Add parallel markings on bases B C D 2 3

7. Proportional Perimeters and Areas Theorem
If the ratio of similar figures is , then the ratio of their perimeters
is , and the ratio of their areas is A D 5 3
Add parallel markings on bases 10 B C 4 6 E F 8