CK-12 Geometry Concepts

4.8. ASA and AAS Triangle Congruence http://www.ck12.org

a)AB∼=U T

b)AC∼=UV

c)BC∼=T V

d)^6 B∼=^6 T

For ASA, we need the side between the two given angles, which isACandUV. The answer is b.

Example B

Write a two-column proof.

Given:^6 C∼=^6 E,AC∼=AE

Prove: 4 ACF∼= 4 AEB

TABLE4.11:

Statement Reason

1.^6 C∼=^6 E,AC∼=AE Given
2.^6 A∼=^6 A Reflexive PoC
3. 4 ACF∼= 4 AEB ASA

Example C

What information do you need to prove that these two triangles are congruent using:

a) ASA?

b) AAS?

a) For ASA, we need the angles on the other side ofEFandQR. Therefore, we would need^6 F∼=^6 Q.

b) For AAS, we would need the angle on the other side of^6 Eand^6 R.^6 G∼=^6 P.

Watch this video for help with the Examples above.

MEDIA

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CK-12 Foundation: Chapter4ASAandAASTriangleCongruenceB

Concept Problem Revisited

Even though we do not know all of the angle measures in the two triangles, we can find the missing angles by using
the Third Angle Theorem. In your parents’ kitchen, the missing angle is 39◦. The missing angle in your neighbor’s
kitchen is 50◦. From this, we can conclude that the two kitchens are now congruent, either by ASA or AAS.