Question

state what additional information is required in order to know that the triangles are congruent for the reason given. 13) asa 14) aas a) \\( \overline { p q } \cong \overline { w v } \\) b) \\( \overline { q r } \cong \overline { v u } \\) c) \\( \overline { r p } \cong \overline { u w } \\) d) \\( \angle q \cong \angle v \\) a) \\( \angle m \cong \angle x \\) b) \\( \overline { m l } \cong \overline { x y } \\) c) \\( \angle n \cong \angle w \\) d) \\( \overline { n m } \cong \overline { w x } \\)

Explanation:

Step1: Recall ASA (Angle - Side - Angle) congruence criterion

ASA states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
For the first pair of triangles, we already have one angle (\(\angle P\)) and one side (marked as equal). We need another angle. If \(\angle Q\cong\angle V\), then we can apply ASA.

Step2: Recall AAS (Angle - Angle - Side) congruence criterion

AAS states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the triangles are congruent.
For the second pair of triangles, we have one angle (\(\angle M\) and the marked side). If \(\angle N\cong\angle W\), then we can apply AAS.

Answer:

1. D. \(\angle Q\cong\angle V\)
2. C. \(\angle N\cong\angle W\)