Question

1. suppose $overline{tm}congoverline{gl}$ and $angle mcongangle g$. what additional information is needed to prove $\triangle mtdcong\triangle gls$ by sas? $overline{td}congoverline{sl}$ $angle tcongangle l$ $overline{md}congoverline{sg}$ $angle tcongangle s$

Explanation:

Step1: Recall SAS congruence criterion

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In \(\triangle MTD\) and \(\triangle GLS\), we already know that \(\overline{TM}\cong\overline{GL}\) and \(\angle M\cong\angle G\). The included sides for the given angles are \(\overline{MD}\) and \(\overline{GS}\) respectively.

Step2: Determine the required side - side congruence

For \(\triangle MTD\cong\triangle GLS\) by SAS, we need the side adjacent to the given congruent angles to be congruent. That is, we need \(\overline{MD}\cong\overline{SG}\).

Answer:

\(\overline{MD}\cong\overline{SG}\)