1. Section 6.6: Using Proportionality Theorems
Chapter 6: Similarity
Section 6.6: Using Proportionality Theorems

2. Section 6.6: Using Proportionality Theorems
Triangle Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
In ΔQRS, if TU || QS, then R T U Q S

3. Section 6.6: Using Proportionality Theorems
Find the value of the variable: Q K 36 y x 10 U L R 14 22 M P S 20 N 10 T

4. Section 6.6: Using Proportionality Theorems
Converse of the Triangle Proportionality Theorem: If a line divides two sides of a triangle proportionally, then it is parallel to the third side
In ΔQRS, if , then TU || QS R T U Q S

5. Section 6.6: Using Proportionality Theorems
Given the diagram, determine whether CD is parallel to EF. B 72 96 C 30 E D 40 F

6. Section 6.6: Using Proportionality Theorems
Midsegment of a triangle: a segment that connects the midpoints of two sides of a triangle
The Midsegment Theorem: The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.
If ΔABC, if CD = DA and CE = EB, then DE || AB and DE = ½ AB C D E A B

7. Section 6.6: Using Proportionality Theorems
Find the length of UY
Find the value of the variable U Y 17 V X W p 16

8. Section 6.6: Using Proportionality Theorems
Theorem: If three parallel lines intersect two transversals, then they divide the transversals proportionally. Y W U V X Z

9. Section 6.6: Using Proportionality Theorems
Using the information in the diagram, find the distance between First Street and Main Street
160 m
320 m 1 2
340 m 3
First Street
Main St
Second St

10. Section 6.6: Using Proportionality Theorems
Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. A C D B

11. Section 6.6: Using Proportionality Theorems
In the diagram, <ABD ≅ <CBD. Use the given side lengths to find the length of DC. B 32 24 A D C 40

12. Section 6.6: Using Proportionality Theorems
Homework: Pg. 400 #3-17 (all)