Question

17
according to the asa criterion, which of the following sets of relationships can be used to show that △vrt and △str are congruent?
○a. ∠srt ≅ ∠vtr and overline{sr} ≅ overline{vt}
○b. ∠str ≅ ∠vtr and ∠srt ≅ ∠vrt
○c. ∠srt ≅ ∠vtr and ∠str ≅ ∠vrt
○d. ∠tvr ≅ ∠rst and overline{vr} ≅ overline{st}

Explanation:

Step1: Recall ASA criterion

ASA (Angle - Side - Angle) criterion 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 two triangles are congruent.

Step2: Analyze each option

• Option A:
• We have \(\angle SRT\cong\angle VTR\) and \(\overline{SR}\cong\overline{VT}\). But we don't have the information about the included side in the correct way for ASA.
• Option B:
• \(\angle STR\cong\angle VTR\) and \(\angle SRT\cong\angle VRT\). There is no information about the included side.
• Option C:
• In \(\triangle VRT\) and \(\triangle STR\), \(\angle SRT\cong\angle VTR\) (given as one angle), \(\overline{RT}\cong\overline{RT}\) (common side, which is the included side), and \(\angle STR\cong\angle VRT\) (another angle). This satisfies the ASA criterion.
• Option D:
• \(\angle TVR\cong\angle RST\) and \(\overline{VR}\cong\overline{ST}\). There is no proper angle - side - angle combination as required by ASA.

Answer:

C. \(\angle SRT\cong\angle VTR\) and \(\angle STR\cong\angle VRT\)