Question

If ∠O≅∠P
and ∠R≅∠R
by the Reflexive Property of Congruence, what additional information is needed to prove ΔNOR≅ΔQPR
by the AAS Congruence Theorem?
Responses

Answer 1

To prove that \(\Delta NOR \cong \Delta QPR\) using the AAS (Angle-Angle-Side) Congruence Theorem, you need the following additional information:

1. **One pair of corresponding sides to be congruent:** You need to know that one pair of non-included sides of the triangles is congruent. This means you need to establish that either side \(NO \cong QP\) or side \(OR \cong PR\).

Given:
- \(\angle O \cong \angle P\) (provided)
- \(\angle R \cong \angle R\) (reflexive property; provided)

You would also need:
- Either \(NO \cong QP\), or \(OR \cong PR\).

Once you have either of these side congruences added to the pair of angle congruences, you can then use the AAS theorem to conclude that \(\Delta NOR \cong \Delta QPR\).