Warm up

3.7 Midsegments of Triangles & Trapezoids

FYI

3.7 today 3.8 next time

Review the time after that... Then… Chapter 3 test the time after that

Midsegment of a triangle

• A segment whose endpoints are the midpoints of two sides. It is parallel to one side of the triangle and its measure is ½ of that side.

A

B

C

D

EX

½ X

If AE = 15

Find the measure of BD

BD = 7.5

midsegment

X + 2

3X - 5A

B

C

D

E3X – 5 = 2(X + 2)

3X – 5 = 2X + 4

X = 9

AE = 22 units

BD = 11

TRY THIS

A

B

C

D

EX2 + 1

X

AND THIS X2 + 1 = 2 (X)

X2 – 2X + 1 = 0

(X – 1) (X – 1) = 0

X = 1

BD = 1 units

AE = 2 units

Midsegment of a Trapezoid

♥ A segment whose endpoints are the midpoints of the NON-PARALLEL sides.

♥ It’s parallel to the bases and ♥ its measure = (Sum of the bases)

2

Midsegment

BASES

Try this Find the lengths of the parallel segments when x = 2

A

B

CZ

Y

MX

X + 5

?

AM = 2

BY = 7

CZ = 12

Check to make sure these numbers work…

Find ? ? = X + 102 + 12 = 7

2

YEA!!YEA!!

Try this…

ZA

B

C

Y

X

If AZ = 25 and

CX = 31, find BY

BY = 28

If AZ = x2 + 4x - 36 and

CX = x2 + 2x - 40 and BY = 16

Find the lengths of the bases

and this…

2(4x-4) = 10x – 12

8x – 8 = 10x -12

4 = 2x

X = 2

BD = 4 AE = 8

Uno mas

Find the lengths of BD and AE if

BD = 4x – 4 and AE = 10x – 12

B

C

D

EA

Assignment

Pg 186, 5-8, 10-16, 22, 28-30, 32-40