Question

in the figure shown, what additional information is needed to show that the triangles are congruent by asa? no additional information needed ∠tuv≅∠muk <t≅ <m (overline{uv}congoverline{uk}) or (overline{vt}congoverline{km}) <yuv≅ <muk

Explanation:

Step1: Recall ASA congruence criterion

ASA (Angle - Side - Angle) states that two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. In the given figure, we have a common side $\overline{UV}=\overline{UK}$ (the tick - marks indicate congruent segments). We need two pairs of congruent angles where the common side is the included side for both pairs.

Step2: Analyze the angle - side - angle requirement

We need to have two pairs of congruent angles with the common side $\overline{UV}$ (or $\overline{UK}$) as the included side. $\angle TUV$ and $\angle MUK$ are vertical angles, so $\angle TUV\cong\angle MUK$. To use ASA, we also need $\angle T\cong\angle M$. Then, with the common side $\overline{UV}=\overline{UK}$, $\triangle TUV\cong\triangle MUK$ by ASA.

Answer:

$\angle T\cong\angle M$