The congruence theorem that can be used to prove that△ABR ≅ △RCA is; HL
- We are told that; △ABR and △RCA share side RA.
From the diagram attached, we can see that RA is the hypotenuse of both triangles.
- From reflexive property, RA is congruent to itself. So we have the hypotenuse of both triangles congruent to each other.
- Now, we are told that ∠BAR and ∠ARC are right angles. This means they are equal and congruent to each other.
- We are also told that sides BR and AC are congruent. Now, from the image attached, we can see that BR and AC are legs of both triangles.
- Thus, the corresponding hypotenuse and corresponding legs of both triangles are congruent.
- In conclusion, the congruency theorem that can be used is HL (Hypotenuse Leg) Theorem which states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then we can say that both triangles are congruent.
Read more on HL Congruence theorem at; https://brainly.com/question/14053210
