Question

f Congruence, what additional information is needed to prove △NOR≅△QPR by the AAS Congruence Theorem? (1 point) Responses NR¯¯¯¯¯¯¯¯≅QP¯¯¯¯¯¯¯¯ line segment cap n cap r is congruent to line segment cap q cap p NO¯¯¯¯¯¯¯¯≅PR¯¯¯¯¯¯¯¯ line segment cap n cap o is congruent to line segment cap p cap r NO¯¯¯¯¯¯¯¯≅QP¯¯¯¯¯¯¯¯ line segment cap n cap o is congruent to line segment cap q cap p OR¯¯¯¯¯¯¯¯≅PR¯¯¯¯¯¯¯¯ line segment cap o cap r is congruent to line segment cap p cap r

Answer 1

if you had to choose one what will it be?

Answer 2

To prove triangles \( \triangle NOR \) and \( \triangle QPR \) are congruent by the AAS (Angle-Angle-Side) Congruence Theorem, you need to establish that two angles and the non-included side of one triangle are congruent to the corresponding angles and the non-included side of the other triangle.

In your options, the side that needs to be shown as congruent is the side that is not included between the two angles.

1. If you already know two angles of each triangle are congruent (let's say \( \angle N \cong \angle Q \) and \( \angle O \cong \angle R \)), then you would need to show that one of the corresponding non-included sides is also congruent.

From your provided options:
- **NR ≅ QP**: This shows the side opposite angle O in △NOR is congruent to the side opposite angle R in △QPR.
- **NO ≅ PR**: This shows the side opposite angle N in △NOR is congruent to the side opposite angle Q in △QPR.
- **NO ≅ QP**: This does not correspond correctly since it matches NO with QP.
- **OR ≅ PR**: This shows the side opposite angle R in △NOR is congruent to the side opposite angle P in △QPR.

To conclude, you need either **NR ≅ QP**, **NO ≅ PR**, or **OR ≅ PR** to complete the proof by AAS. If we have already established the angles are congruent, identifying any of these sides as congruent will allow you to prove \( \triangle NOR \cong \triangle QPR \) by AAS.

Answer 3

If I had to choose just one option to establish congruence using the AAS Congruence Theorem, I would select:

**NO ≅ PR**

This is because it provides the necessary non-included side congruence that complements the two angles already assumed to be congruent, thereby fulfilling the requirements of the AAS theorem effectively.