Question

Based only on the information given in the diagram, which congruence theorems could be given as reasons why ABC ~ UVW? Check all that apply.

A. SAS
B. ASA
C. AAS
D. LA
E. LL
F. HL.
[Check all that apply.]

Answer 1

The right answers are LA and ASA

Answer 2

(B) and (D)

Explanation:

It is given that there are two triangles ABC and UVH, then

From ΔABC and ΔUVH, we have

∠A=∠U(Each90°)

AC=UH (Given)

∠C=∠H (Given)

Thus, by ASA rule of congruency,

ΔABC≅ΔUVH

Also, From ΔABC and ΔUVH, we have

If the leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent, thus

AC=UH, then ΔABC≅ΔUVH (By LA rule)

therefore, option B and D are correct.