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 included - side relationship with another pair of angles for ASA.
• Option B:
• \(\angle STR\cong\angle VTR\) and \(\angle SRT\cong\angle VRT\). The side between \(\angle SRT\) and \(\angle VRT\) is not the same as the side between \(\angle STR\) and \(\angle VTR\) for ASA.
• Option C:
• \(\angle SRT\cong\angle VTR\), \(\angle STR\cong\angle VRT\), and \(\overline{RT}\cong\overline{RT}\) (common side). Here, \(\angle SRT\), \(\overline{RT}\), \(\angle STR\) in \(\triangle STR\) and \(\angle VTR\), \(\overline{RT}\), \(\angle VRT\) in \(\triangle VRT\) satisfy the ASA criterion.
• Option D:
• \(\angle TVR\cong\angle RST\) and \(\overline{VR}\cong\overline{ST}\). This does not match the ASA (angle - side - angle) pattern.

Answer:

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