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# 4-4 Proving Congruence- SSS, SAS - PowerPoint PPT Presentation

4-4 Proving Congruence- SSS, SAS. Congruent. Means that corresponding parts are congruent, Matching sides and angles will be congruent. B. A. C. Y. X. Z. Naming. ORDER MATTERS!!!!. Example 1. If two triangles are congruent… Name all congruent angles Name all congruent sides. R.

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### 4-4 Proving Congruence- SSS, SAS

• Means that corresponding parts are congruent,

• Matching sides and angles will be congruent

A

C

Y

X

Z

• ORDER MATTERS!!!!

• If two triangles are congruent…

• Name all congruent angles

• Name all congruent sides

R

X

S

T

Y

Z

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

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

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

X

Y

B

A

Z

C

• 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.

B

D

E

F

C

A

RQ||TS

Given

Alt. int. <‘s are congruent

Given

Reflexive

R

S

SAS

Q

T

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

Prove:

D

E

C

G

Statement

Reason

• Given

• Def. of Isosceles Triangle

• Midpoint theorem

• Reflexive property

• SSS

1

Triangle CDE is isosceles

2

CD = ED

3

CG = GE

4

DG = DG

5

### 4-5 Proving CongruenceASA and AAS

• 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.

Prove:

E

R

L

D

W

<W <E because_________________ angles are ____________. By the___________________,

WL___EL. Since vertical angles are _____________,

______________ and by ______

Alternate interior

Congruent

Def. of midpoint thrm

Congruent

=

<RLW = <ELD

ASA

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

Prove:

K

J

M

L

N

Statement

Reason

Given

1. <NKL <NJM

1. ____________

2. <N <N

Reflexive

2.____________

KL = MN

3._____________

3. Given

4. AAS

4.

5. CPCTC

5.___________