Properties of Triangles

Chapter 5

5.4 Midsegment Theorem

State Standards for Geometry17. Prove theorems using

coordinate geometry.

Lesson Goals• Identify the midsegments

of a triangle.• Discover the

Midsegment theorem• Use properties of

midsegments of a triangle to solve problems.

ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

definitionMidsegment of a Triangle A segment that connects the midpointsof two sides of a triangle.

is a midsegment for .ED ABCA

BC D

E

Discovering the Midsegment Theorem

21

2

3 1

2 6STm

41

4

AB STThe slopes are the same which means .

example

.ABc. Find and ST

2 23 1 2 0AB

4 4 8 2 2

2 26 2 1 3ST

16 16 32 4 2

.ST ABis twice the length of .AB STor is half the length of

then DE AB

theoremMidsegment Theorem

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.

If is a midsegment of DE ABCA

BC D

E

12and DE AB

List all segments that are parallel to each other.

example

LM SR

QS MN

LN QR

and are midsegments of . Find and .JK KL ABC

JK AC

A

BC L

KJ

10

3

example

12JK CB

12 10JK

5JK

12KL AC123 AC

6 AC

Today’s Assignment

p 290: 1, 2, 10 – 17, 19, 28, 29