Question

1. suppose \\( \overline { tm } \cong \overline { gl } \\) and \\( \angle m \cong \angle g \\). what additional information is needed to prove \\( \triangle mtd \cong \triangle gls \\) by sas?

\\( \angle t \cong \angle l \\)
\\( \angle t \cong \angle s \\)
\\( \overline { md } \cong \overline { sg } \\)
\\( \overline { td } \cong \overline { sl } \\)

Explanation:

Step1: Recall SAS (Side - Angle - Side) congruence criterion

For two triangles \(\triangle MTD\) and \(\triangle GLS\), SAS congruence requires two sides and the included angle of one triangle to be congruent to the corresponding two sides and included angle of the other triangle. We know \(TM\cong GL\) (given as a side) and \(\angle M\cong\angle G\) (given as an angle).

Step2: Identify the missing side

The sides adjacent to the given angles in \(\triangle MTD\) and \(\triangle GLS\) are \(MD\) and \(GS\) respectively. For SAS congruence (\(TM\cong GL\), \(\angle M\cong\angle G\)), we need \(MD\cong GS\)

Answer:

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