Topic: U7L5 Proving Congruence--SSS, SAS

EQ: What is meant by SSS and SAS and how do I use them in

proofs?

Congruent Triangles

• Means that corresponding parts are congruent,

• Matching sides and angles will be congruent

A

B

C

Z

Y

X

Naming

• ORDER MATTERS!!!!

Example 1

• If two triangles are congruent…– Name all congruent angles

– Name all congruent sides

S

R

T

Y

X

Z

Reminder…

• If two angles of one triangle are congruent to two angles of another triangle then the 3rd angles are congruent

Keep in mind

• You can flip, turn or slide congruent triangles and they will maintain congruency!!

Side-Side-Side Congruence (SSS)

• If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent

A

B

C

X Y

Z

XYZABC

Included angles

Side-Angle-Side Congruence (SAS)

• If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

A

B

C

DE

F

FDEABC

Given: Triangle CDE is an isosceles triangle. G is the midpoint of CE.

Prove:

CG

E

D

EDGCDG

Statement Reason

1. Given

2. Def. of Isosceles Triangle

3. Midpoint theorem

4. Reflexive property

5. SSS

1

2

3

4

5

Triangle CDE is isosceles

CD = ED

CG = GE

DG = DG

EDGCDG