1. Lesson 7-6 Proportional Lengths (page 254)
Essential Question
How do you calculate the lengths of sides of similar triangles?

2. If AB : BC = XY : YZ, then AC and XZ
are said to be divided proportionally . A B C X Y Z

3. Theorem 7-3 Triangle Proportionality Theorem ➤ ➤
If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally . T
Given: ∆ RST; PQ || RS
Prove: P ➤ Q ➤ S R

4. Triangle Proportionality Theorem
Given: ∆ RST; PQ || RS
Prove:
PT QT
RP SQ T
Top Left
Top Right P ➤ Q
Bottom Left
Bottom Right ➤ S R

5. many equivalent proportions can be justified …
NOTE: Since ∆RST ~ ∆PQT,
many equivalent proportions can be justified … T P ➤ Q ➤ S R
by the AA ~ Postulate

6. ➤ ➤ Here are many equivalent proportions along with
informal statements
describing them. P ➤ Q ➤ S R

7. T P ➤ Q ➤ S R

8. T P ➤ Q ➤ S R

9. T P ➤ Q ➤ S R

10. This is the only way to get the parallel sides.➤ Q ➤ S R
DO NOT
FORGET
THESE
RATIOS!
This is the only way to get the parallel sides.

11. Example #1. Find the value of “x”.20 15 ➤ 8 x ➤

12. Theorem REVIEW!!!
If three parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
Given:
Prove: A ➤ X B ➤ Y C ➤ Z

13. Corollary
If three parallel lines intersect two transversals, then they divide the transversals proportionally . R ➤ X
Given:
Prove: S ➤ Y T ➤ Z

14. ➤ ➤ ➤ Example #2. Find the value of “x”. 25 - x = 20 25 - x 16 x = 5 x4 ➤

15. Theorem 7-4 Triangle Angle-Bisector Theorem DG bisects ∠FDE
If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides . F
Given: ∆ DEF ;
DG bisects ∠FDE
Prove: G E D

16. Example #3. Find the value of “x”.27 45 x
= 15
40 - x
= 25 40

17. Example #4. Find the value of “x”.12 18 x 24

18. How do you calculate the lengths of sides of similar triangles?
Assignment
Written Exercises on pages 272 & 273
DO NOW: 1 to 11 ALL numbers
GRADED: 13, 15, 17, 21, 23
YOU MUST SHOW YOUR WORK & DIAGRAM!
Prepare for Quiz on Lessons 7-4 to 7-6
How do you calculate the lengths of sides of similar triangles?

19. How do you use similar polygons to solve real life problems?
Prepare for Test on
Chapter 7: Similar Polygons
Chapter Review on pages 277 & 278:
4, 12, 16 – 20,
Chapter Test on page 279: 1,
How do you use similar polygons to solve real life problems?