1. 4.3: Theorems about Proportionality
WELCOME
4.3: Theorems about Proportionality
Last Night’s HW: 4.2 Handout
Tonight’s HW: 4.3 Handout

2. Warm Up
1. Are the triangles similar? If so explain how you know. Write a similarity statement: ∆______~∆_______ 2. Given the figures are similar. Find the missing side length.

3. Homework Review

4. Proof Review

5. Chapter 4.3 Learning Targets

6. Angle Bisector Proportionality
If a ray bisects an angle of a triangle, then it divides the side into segments whose lengths are proportional to the lengths of the other two sides. A D C B
AD CA
If CD bisects ∠ ACB, then =
DB CB

7. Example 2:
Example 1:

8. Triangle Proportionality
If a line is ‖ to a side of a ∆ & intersects the other sides, then it divides them proportionally.
If a line divides two sides of a ∆ proportionally, then it is parallel to the third side. Q Q T T R R U U S S
RT RU
RT RU
If TU ‖ QS, then =
If = , then TU ‖ QS
TQ US
TQ US

9. Example 3:
Example 4:

10. Parallel Line Proportionality
If three parallel lines intersect two transversals, then they divide the transversals proportionally. s t r U l W Y Z m X V
UW VX
If r ‖ s and s ‖ t, then =
WY XZ

11. Example 5:

12. Midsegment of a Triangle
A segment that connects the midpoints of two sides of a ∆ D F E
DE , EF , FD are Midsegment

13. Theorem 5.9 Midsegment Theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long. C E D 8 A B 16 1 2
DE ‖ AB and DE = AB

14. Example 6:
Find x