Question

Based only on the information given in the diagram, which congruence

theorems or postulates could be given as reasons why AABC=AUVW?
Check all that apply.
AA
A. SAS
B. HL
C. ASA
D. AAS
E. LL
F. LA

Answer 1

Based on the information given, the congruence theorems applicable to triangles ABC and UVW are HL (Hypotenuse-Leg) and AA (Angle-Angle), as AC = UW, angle BCA = angle VWU, and angles BAC and VUW are both right angles.

The congruence theorems or postulates that could be used to show that triangle ABC is congruent to triangle UVW, based on the given information, are:

1. **HL (Hypotenuse-Leg):** If the hypotenuse and a leg of one right-angled triangle are congruent to the hypotenuse and corresponding leg of another right-angled triangle, then the triangles are congruent.

2. **AA (Angle-Angle):** If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In this case, the right angles BAC and VUW are congruent, and the angle BCA is congruent to angle VWU.

So, the applicable choices are:

- B. HL

- A. AA