4.4. Triangle Congruence Using ASA, AAS, and HL http://www.ck12.org
Angle-Side-Angle (ASA) Congruence Postulate:If two angles and the included side in one triangle are congruent
to two angles and the included side in another triangle, then the two triangles are congruent.
The markings in the picture are enough to say 4 ABC∼= 4 XY Z.
Now, in addition to SSS and SAS, you can use ASA to prove that two triangles are congruent.
Example 1: What information would you need to prove that these two triangles are congruent using the ASA
Postulate?
a)AB∼=U T
b)AC∼=UV
c)BC∼=T V
d)^6 B∼=^6 T
Solution:For ASA, we need the side between the two given angles, which isACandUV. The answer is b.
Example 2:Write a 2-column proof.
Given:^6 C∼=^6 E,AC∼=AE
Prove: 4 ACF∼= 4 AEB
TABLE4.10:
Statement Reason1.^6 C∼=^6 E,AC∼=AE Given
2.^6 A∼=^6 A Reflexive PoC
(^224) 3. 4 ACF∼= 4 AEB ASA