Question

1. in the diagram, $\triangle mtdcong\triangle slg$. which statement is true? $angle scongangle t$ $angle lcongangle d$ $overline{lg}congoverline{td}$ $overline{sg}congoverline{mt}$

Explanation:

Step1: Recall congruent - triangle property

Corresponding parts of congruent triangles are congruent (CPCTC). For \(\triangle MTD\cong\triangle SLG\), the vertices are paired as \(M\) with \(S\), \(T\) with \(L\), and \(D\) with \(G\).

Step2: Analyze each option

• For \(\angle S\cong\angle T\), the corresponding angles are \(\angle S\) and \(\angle M\), not \(\angle S\) and \(\angle T\), so this is false.
• For \(\angle L\cong\angle D\), the corresponding angles are \(\angle L\) and \(\angle T\), not \(\angle L\) and \(\angle D\), so this is false.
• For \(\overline{LG}\cong\overline{TD}\), since \(\triangle MTD\cong\triangle SLG\), the corresponding sides are \(\overline{LG}\) and \(\overline{TD}\) (corresponding - side pairs are \(MT\) and \(SL\), \(TD\) and \(LG\), \(MD\) and \(SG\)), so this is true.
• For \(\overline{SG}\cong\overline{MT}\), the corresponding sides are \(\overline{SG}\) and \(\overline{MD}\), not \(\overline{SG}\) and \(\overline{MT}\), so this is false.

Answer:

\(\overline{LG}\cong\overline{TD}\)