Question

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

Answer 1

They are congruent by SAS postulate.

Explanation:

Choice for this question are

• HL
• SAS
• SSS
• ASA
• AAS

In the image attached, you can observe the pairs of triangles we are talking about. Notice that they are right triangles, which means the congruence postulates we could use are Hypothenuse-Leg, Leg-Leg, Leg-Angle and Hypothenuse Angle, however, this choices are not useful.

We know by given that

`AC \cong AB` and
`RC \cong RB`

We also know that
`\angle B \cong \angle C`

So, we have two corresponding sides congruent, and the pair of corresponding angle formed by those sides are also congruent.

Therefore, by Side-Angle-Side

`\triangle ABR \cong \triangle ACR`

So, the right answer is SAS.

Answer 2

SAS , ASA, SSS

Explanation:

SAS , side A= side A . Angle B= Angle C, side R= side R

ASA, Angle A= Angle A . Side B= side C, Angle R= Angle R

SSS

side A= side A . Side B= side c, side R= side R