Question

Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why triangle ABC~UVW?

Check all that apply.

A. AAS
B. LL
C. LA
D. HL
E. ASA
F. SAS

Answer 1

(C) and (E)

Explanation:

Given: ΔABC and ΔUVW, AC=UW, ∠A=∠U=90° and ∠C=∠W.

To Prove: ΔABC≅ΔUVW

Solution:

From ΔABC and ΔUVW,

∠A=∠U=90° (Given)

AC=UW (Given)

∠C=∠W (Given)

Thus, by ASA rule of congruency, ΔABC≅ΔUVW

Also, from ΔABC and ΔUVW,

AC=UW (Given)

∠C=∠W (Given)

Thus, by LA rule of congruency , ΔABC≅ΔUVW

Therefore, option C and E are correct.

Answer 2

LA because we know its a right angle and there are a leg and angle congruent on both triangles. AC=UW and C=W.

and ASA because there are 2 angles which are the same with a side in between. A=U, AC=UW, and C=W.