Question

State what additional information is required in order to know that the triangles are congruent by AAS..

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Answer 1

`\overline{vw} \cong \overline{rw}`

Explanation:

AAS tells us that two traingles are coungruent if two angles are congruent and their corresponding opposite sides are congruent. From the picture we know that the segments
`\overline{xv}` and
`\line{RT}` are parallel, hence
`\angle X \cong \angle T` and
`\angle V \cong \angle R`. Moreover, since the two angles
`\angle VWX` and
`\RWT` are opposite by a vertex, they are also congruent.

On the other hand, the picture tells us that
`\overline{wx}\cong\overline{wt}`. Therefore, since we already know that
`\angle VWX \cong \angle RWT` and that
`\angle R \cong \angle V`, we are only missing the information that
`\overline{vw} \cong \overline{rw}` to know that
`\triangle XWV \cong \triangle RWT` by AAS.

Answer 2

You are given that XW and WT are similar and they share and angle W.

You need to know another set of sides are similar.

The answer would be C. VW ≅ RW