4-4 Proving Congruence- SSS, SAS

Congruent

• 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 that RQ||TS and RQ TS, Prove STRQRT

RQ||TS

TSRQ

STRQRT

TRRT

STRQRT

Given

Given

Alt. int. <‘s are congruent

Reflexive

SAS

Q

R S

T

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

4-5 Proving CongruenceASA and AAS

Angle-Side-Angle Congruence(ASA)

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

Given: L is the midpoint of WE and WR||EDProve: EDLWRL

W

RL

D

E

<W <E because_________________ angles are ____________. By the___________________, WL___EL. Since vertical angles are _____________,______________ and by ______EDLWRL

Alternate interior

Congruent Def. of midpoint thrm

= Congruent

<RLW = <ELD ASA

Angle-Angle-Side Congruence(AAS)

• If 2 angles and a non-includednon-included side of one triangle are congruent to the corresponding 2 angles and side of another triangle, then the 2 triangles are congruent.

Given: <NKL <NJM and Prove:

MNKL MNLN

J

L

N

M

K

Statement Reason

1. <NKL <NJM

1. ____________

2. <N <N 2.____________

3._____________ 3. Given

4. 4. AAS

5.___________ 5. CPCTC

KNLJMN

Given

Reflexive

KL = MN

MNLN