1. 8.5 Three Theorems Involving Proportion
Objective:
After studying this section, you will be able to apply three theorems frequently used to establish proportionality.

2. (Side-Splitter Theorem)
Theorem If a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally.
(Side-Splitter Theorem) A
Given: BE ll CD E B
Prove: C D

3. Theorem. If three or more parallel lines are
Theorem If three or more parallel lines are intersected by two transversals, the parallel lines divide the transversals proportionally. A B
Given: AB ll CD ll EF C G
Prove: D E F

4. Theorem. If a ray bisects an angle of a
Theorem If a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides.
(Angle Bisector Theorem)

5. Given: A 1 2
Prove: B D C

6. Given: BE ll CD
lengths as shown A 7 4 6
Find: a. ED
b. CD E B 2 C D

7. Given: a ll b ll c ll d lengths as shown KP = 24 Find: KM F K a 5 M b8 J P d

8. V
Given:
lengths as shown 8 10
Find: ST R 4 S x T

9. Given: W
Conclusion: A X Y Z

10. Given: C D H B E
Prove: F G

11. Summary: In your own words, state how you can apply the three theorems learned in this lesson.
Homework: worksheet