over lesson 7–4 5-minute check 4 if ab = 4, bc = 7, ed = 5, and ec = 13.75, determine whether bd...

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Over Lesson 7–4 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.

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Page 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

Over Lesson 7–4

If AB = 4, BC = 7, ED = 5, and EC = 13.75, determinewhether BD || AE.

___ ___

In the diagram, 1st Street is parallel to 3rd Street and 5th Street. Find the distance from 3rd Street to 5th Street if you are traveling on 4th Street.

Page 2: 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

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.

Page 3: 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

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.

Page 4: 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

Can you identify what special triangle segment that is drawn in each category?

1) 2)

3)

Page 5: 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

• 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…

Page 6: 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

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?

Page 7: 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

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!)

Page 8: 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

Example

• Find the altitude QS.

2

3

16

24

TR

NP

x

6

2

3

4

123

x

x

N M P

Q

R S T

24

6

16

Page 9: 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

Medians of Similar Triangles

Answer: JL = 28.

EG

Page 10: 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

1. A

2. B

3. C

4. D

A. 2.8

B. 17.5

C. 3.9

D. 0.96

Page 11: 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

Use Special Segments in Similar Triangles

In the figure, ΔLJK ~ ΔSQR. Find the value of x.

Answer: x = 7.5

Page 12: 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

A. 10.5 in

B. 61.7 in

C. 21 in

D. 28 in

Page 13: 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

Page 14: 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

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

Page 15: 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

Find n.

Page 16: 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

3-2-1 Exit Slip

3 things you have learned the past 2 days2 things you are still not sure about/comments*

1 question you have**If none, then write “none”

Homework: pg. 505 #10, 22-24

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