Question

in the diagram, $\triangle mtdcong\triangle gls$. which statement is true?
$angle mcongangle g$
$angle tcongangle s$
$overline{dm}congoverline{sl}$
$overline{dt}congoverline{lg}$

Explanation:

Step1: Recall the properties of congruent triangles

When \(\triangle MTD\cong\triangle GLS\), the corresponding parts (angles and sides) are congruent. That is, \(\angle M\cong\angle G\), \(\angle T\cong\angle L\), \(\angle D\cong\angle S\), \(\overline{MT}\cong\overline{GL}\), \(\overline{TD}\cong\overline{LS}\), and \(\overline{DM}\cong\overline{SG}\).

Step2: Check each option

• For \(\angle M\cong\angle G\): Since \(\triangle MTD\cong\triangle GLS\), by the definition of congruent triangles (corresponding angles of congruent triangles are congruent), \(\angle M\) and \(\angle G\) are corresponding angles.
• For \(\angle T\cong\angle S\): \(\angle T\) corresponds to \(\angle L\) (not \(\angle S\)) in \(\triangle GLS\) as per the congruence \(\triangle MTD\cong\triangle GLS\).
• For \(\overline{DM}\cong\overline{SL}\): \(\overline{DM}\) corresponds to \(\overline{SG}\) (not \(\overline{SL}\)) in \(\triangle GLS\) as per the congruence \(\triangle MTD\cong\triangle GLS\).
• For \(\overline{DT}\cong\overline{LG}\): \(\overline{DT}\) corresponds to \(\overline{LS}\) (not \(\overline{LG}\)) in \(\triangle GLS\) as per the congruence \(\triangle MTD\cong\triangle GLS\).

Answer:

\(\angle M\cong\angle G\)