Question

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

Explanation:

Step1: Recall ASA congruence criterion

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

Step2: Analyze given in the figure

We can assume the two right - angles at R and C are equal. We need the included side between another pair of angles and one of the right - angles to be congruent. So we need to know that $\angle RCT=\angle ECR$ and $RC = RC$ (common side) or $\angle REC=\angle TCR$ and $RC = RC$ (common side). In other words, we need to know that $\angle RCT=\angle ECR$ (or $\angle REC=\angle TCR$) since the common side $RC$ is already there.

Answer:

We need to know that $\angle RCT=\angle ECR$ (or an equivalent angle - equality statement that gives the second pair of angles with the included side $RC$).