Over Lesson 7–3

Complete the proportion.

Suppose DE=15, find x.

Suppose DE=15, find EG.

Find the value of y.

FEFE

33

1212

1818

Ch 9.5

D

F

G

EH

x

2 8

DG = FHDE ?

12 14

y

y + 3

Ch 9.5Proportional Parts

Standard 7.0Students use theorems involving the properties of

parallel lines cut by a transversal.

Learning Target:I will be able to use proportions to determine whether lines are parallel to sides of triangles.

Ch 9.5

midsegment of a triangle

A segment of a triangle is called a midsegment when its endpoints are the midpoints of two sides of the triangle.

Ch 9.5

A

B C

Midpoint of AB Midpoint of AC

Ch 9.5

Theorem 9-6

Determine if Lines are Parallel

In order to show that we must show that

Ch 9.5

Since the sides are proportional.

Answer: Since the segments have

proportional lengths, GH || FE.

A. yes

B. no

C. cannot be determined

Ch 9.5

Ch 9.5

Theorem 9-7

Use the Triangle Midsegment Theorem

A. In the figure, DE and EF are midsegments of ΔABC. Find AB.

Ch 9.5

ED = AB Triangle Midsegment Theorem

__12

5 = AB Substitution__12

10 = AB Multiply each side by 2.

Answer: AB = 10

Use the Triangle Midsegment Theorem

B. In the figure, DE and EF are midsegments of ΔABC. Find FE.

Ch 9.5

FE = (18) Substitution__12

__12

FE = BC Triangle Midsegment Theorem

FE = 9 Simplify.

Answer: FE = 9

Use the Triangle Midsegment Theorem

C. In the figure, DE and EF are midsegments of ΔABC. Find mAFE.

Ch 9.5

AFE FED Alternate Interior Angles Theorem

mAFE = mFED Definition of congruence

mAFE = 87 Substitution

By the Triangle Midsegment Theorem, AB || ED.

Answer: mAFE = 87

A. 8

B. 15

C. 16

D. 30

A. In the figure, DE and DF are midsegments of ΔABC. Find BC.

Ch 9.5

B. In the figure, DE and DF are midsegments of ΔABC. Find DE.

A. 7.5

B. 8

C. 15

D. 16

Ch 9.5

C. In the figure, DE and DF are midsegments of ΔABC. Find mAFD.

A. 48

B. 58

C. 110

D. 122

Ch 9.5