4.4. Triangle Congruence Using ASA, AAS, and HL http://www.ck12.org
By proving 4 ABC∼= 4 Y ZXwith ASA, we have also shown that the AAS Theorem is valid. You can now use this
theorem to show that two triangles are congruent.
Example 3:What information do you need to prove that these two triangles are congruent using:
a) ASA?
b) AAS?
c) SAS?
Solution:
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.
c) For SAS, we would need the side on the othersideof^6 Eand^6 R. So, we would needEG∼=RP.
Example 4:Can you prove that the following triangles are congruent? Why or why not?
Solution:Even thoughKL∼=ST, they are not corresponding. Look at the angles aroundKL,^6 Kand^6 L.^6 Khas
onearc and^6 Lis unmarked. The angles aroundSTare^6 Sand^6 T.^6 Shastwoarcs and^6 Tis unmarked. In order to
use AAS,^6 Sneeds to be congruent to^6 K. They are not congruent because the arcs marks are different. Therefore,
we cannot conclude that these two triangles are congruent.
Example 5:Write a 2-column proof.
Given:BDis an angle bisector of^6 CDA,^6 C∼=^6 A