Question

What additional piece of information would you need to use the Side-Angle-Side Triangle Congruence Postulate to prove that △RQP ≅ △SQP?

Answer 1

`RQ = SQ`

Explanation:

Given

△RQP ≅ △SQP

See attachment

Required

Additional information that shows that △RQP ≅ △SQP

△RQP and △SQP share a common side QP:

This implies that:

`QP = QP` ---- Side (S)

△RQP ≅ △SQP implies that:

`\angle RQP = \angle SQP` ---- Angle (A)

Lastly, we already established that △RQP and △SQP share a common side QP

Then remove point P, we have: RQ and SQ

This implies that:

`RQ = SQ` --- Side (S)

Hence, the additional piece of information needed is:
`RQ = SQ`