Question

question
what additional piece of
mark any congruent parts on the triangles that can be proved.
information is required to prove the triangles congruent by asa ≅?

Explanation:

Step1: Recall ASA congruence criterion

ASA (Angle - Side - Angle) congruence criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
In triangles \( \triangle TDS\) and \( \triangle TDD\) (assuming the two triangles are \( \triangle TDC\) and \( \triangle TSC\) from the figure), we already have one pair of angles (marked in the figure) and the common side \(TC = TC\) (reflexive property \(a=a\)).

Step2: Identify the required angle

We need another pair of angles. Since \( \angle DTC\) and \( \angle STC\) can be the other pair of angles. If \( \angle DTC=\angle STC\), then by ASA (\( \angle DCT=\angle SCT\), \(TC = TC\), \( \angle DTC=\angle STC\)) the two triangles \( \triangle TDC\) and \( \triangle TSC\) will be congruent.

Answer:

\(\angle DTC\cong\angle STC\)