5.1: Midsegments of Triangles

Objectives:To use properties of midsegments to solve problems

Warm-Up

1. Find the distance between the 2 points A(-1,-4) and B(2, 3).

2. Find the coordinates of the midpointof the segment with endpoints A(-2, 3)and B(4, 1)

Midsegment of a Triangle

Segment connecting the midpoints of 2 sides of a triangle

A

D

B

E

C

D is the midpoint ofE is the midpoint of is the midsegment of

AB

BC

DE ABC

Triangle Midsegment Theorem

If a segment joins the midpoints of 2 sides of a triangle, the segment is parallel to the 3rd side, and is ½ its length

Do NOT assume it’s a midsegment unless they tell you or you prove it.

Triangle Midsegment Theorem

is the midsegment of Therefore…. AND

DE ABC

ABDE || ABDE2

1

EXAMPLES: Find the value of the variables.

1. 2.

D

A

E

B Cx

18

x+2

20

Find the perimeter of ADE

A

D

E

53

7

Find the value of the variable.

(6x)°

30°

In ∆XYZ, M, N, and P are midpoints. The perimeter of the ∆ MNP is 60 yd. Find NP and YZ.

X

YZ

M P

N

22

24

NAME ALL PARALLEL SEGMENTS:

What is the measure of angle ANM? Angle A? Explain.

A

M

BC

N

65°