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4-4 Proving Congruence- SSS, SASPowerPoint Presentation

4-4 Proving Congruence- SSS, SAS

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### 4-5 Proving CongruenceASA and AAS

Congruent

- Means that corresponding parts are congruent,
- Matching sides and angles will be congruent

Naming

- ORDER MATTERS!!!!

Example 1

- If two triangles are congruent…
- Name all congruent angles
- Name all congruent sides

R

X

S

T

Y

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

X

Y

B

A

Z

C

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.

B

D

E

F

C

A

Given that RQ||TS and RQ TS, Prove

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

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||ED

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

Angle-Angle-Side Congruence(AAS)

- 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.___________

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