4.4 Proving Triangles are Congruent: ASA and AAS - Summer Geometry

[Pages:8]NOTES 4.4 ? 4.5

Triangle Congruence SSS, SAS, ASA, AAS, HL

Objectives:

1. Prove that triangles are congruent using the SSS, SAS, ASA, AAS, and HL Congruence Postulates

2. Use congruence postulates and theorems in real-life problems.

SSS (Side-Side-Side) Postulate

If 3 sides of one triangle are congruent to 3

sides of another triangle, then the triangles

are congruent.

A

Y

X

Z

B

C

ABC = XYZ

SAS (Side-Angle-Side)

Postulate

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

Y

X

Z

B

C

ABC = XYZ

ASA (Angle-Side-Angle) Postulate

? If two angles and the

B

included side of one

triangle are

A

congruent to two

E

angles and the

C

included side of a

F

second triangle, then

the triangles are

D

congruent.

AAS (Angle-Angle-Side) Theorem

? If two angles and a

B

non-included side of

one triangle are

A

congruent to two angles and the

E

corresponding non- C

F

included side of a

second triangle, then

the triangles are

D

congruent.

HL (Hypotenuse - Leg) Theorem:

? If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle, then the two triangles are congruent.

? Example: ABC XYZ because of HL.

A

X

B

C

Y

Z

Triangles are congruent by...

SSS

AAS

SAS

ASA

HL

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