Question

Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.

Triangles A B R and A C R share side A R. Angles A B R and A C R are right angles. Sides A B and A C are congruent. Sides B R and C R are congruent.

HL
SAS
SSS
ASA
AAS

Answer 1

HL, SAS, SSS

Reasoning (brief):
- HL: Both triangles are right (∠ABR = ∠ACR = 90°), share hypotenuse AR, and have BR = CR, so hypotenuse-leg applies.
- SAS: AB = AC and BR = CR, and the included angles ∠ABR and ∠ACR are both 90°, so SAS applies.
- SSS: AB = AC, BR = CR, and AR = AR (common), so SSS applies.