1. Over Lesson 7–4 5-Minute Check 4 If AB = 4, BC = 7, ED = 5, and EC = 13.75, determine whether BD || AE. ___ In the diagram, 1 st Street is parallel to 3 rd Street and 5 th Street. Find the distance from 3 rd Street to 5 th Street if you are traveling on 4 th Street.

2. CCSS Content Standards G.SRT.4 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others.

3. Then/Now 7.5: Parts of Similar Triangles I will be able to… Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles. Solve for missing parts using the Triangle Bisector Theorem.

4. Can you identify what special triangle segment that is drawn in each category? 1)2) 3)

5. What is a median? Segment drawn from a vertex to the midpoint of the opposite side What is an altitude? Segment drawn from a vertex that is perpendicular to the opposite side What is an angle bisector? Segment that bisects an angle and is drawn to the opposite side Recall…

6. Key Question: Based on what we’ve learned the past few days, how do you think the altitudes, medians, and angle bisectors are related between similar triangles?

7. Similar Triangle Proportionality If two triangles are similar, then the ratio of any two corresponding lengths (including altitudes, medians and angle bisector segments) is equal to the scale factor of the similar triangles (aka proportional!)

8. Example Find the altitude QS. NMP Q RST 24 6 16

9. Lesson 5 Ex3 Medians of Similar Triangles Answer: JL = 28. EG

10. 1.A 2.B 3.C 4.D Lesson 5 CYP3 A.2.8 B.17.5 C.3.9 D.0.96

11. Example 1 Use Special Segments in Similar Triangles In the figure, ΔLJK ~ ΔSQR. Find the value of x. Answer: x = 7.5

12. Lesson 5 CYP4 A.10.5 in B.61.7 in C.21 in D.28 in

13. Concept

14. Example 3 Use the Triangle Angle Bisector Theorem Find x. Since the segment is an angle bisector of the triangle, the Angle Bisector Theorem can be used to write a proportion. Answer: x = 10

15. Example 3 Find n.

16. 3-2-1 Exit Slip 3 things you have learned the past 2 days 2 things you are still not sure about/comments* 1 question you have* *If none, then write “none” Homework: pg. 505 #10, 22-24