Question

20 what additional information is needed to prove that the triangles are congruent by asa?

Explanation:

Step1: Recall ASA congruence criterion

ASA (Angle - Side - Angle) requires two pairs of congruent angles and the included side between them to be congruent.

Step2: Analyze given information

We can assume we may have one pair of angles (not clear from the image which ones exactly) and the side \(SC\) is marked. We need the angles adjacent to side \(SC\) in both triangles to be congruent. So we need to know that \(\angle RSC=\angle TCS\) and \(\angle SCR = \angle CST\). Since we likely have some existing angle - related information (not shown fully), if we know that \(\angle RSC=\angle TCS\).

Answer:

The measure of the angles adjacent to the common side \(SC\) in both triangles, specifically that \(\angle RSC=\angle TCS\) and the other pair of adjacent angles \(\angle SCR=\angle CST\) (assuming some partial angle - related info is already given).