Question

20
according to the aas corollary, which of the following sets of relationships can be used to show that △vrt and △str are congruent?
○a. ∠tvr≅∠srt and ∠vtr≅∠rts
○b. ∠srt≅∠vtr and \overline{vt}≅\overline{sr}
○c. ∠str≅∠vrt and \overline{vr}≅\overline{st}
○d. ∠rst≅∠tvr and ∠str≅∠vrt

Explanation:

Step1: Recall AAS (Angle - Angle - Side) congruence

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 two triangles are congruent.

Step2: Analyze each option

• Option A: Only two angles are given. There is no information about a side, so AAS cannot be applied.
• Option B: One angle and one side are given. We need two angles and a non - included side.
• Option C: One angle and one side are given. We need two angles and a non - included side.
• Option D: \(\angle RST\cong\angle TVR\) and \(\angle STR\cong\angle VRT\) (two angles). Also, \(RT = RT\) (common side, which is a non - included side for the two pairs of angles). So, by AAS, \(\triangle VRT\cong\triangle STR\)

Answer:

D. \(\angle RST\cong\angle TVR\) and \(\angle STR\cong\angle VRT\)