Question

1. in the diagram, △mtd≅△slg. which statement is true?

○ overline{mt}congoverline{gl}
○ overline{td}congoverline{sg}
○ ∠mcong∠g
○ ∠tcong∠l

Explanation:

Step1: Recall congruent - triangle properties

When $\triangle MTD\cong\triangle SLG$, corresponding parts of congruent triangles are congruent (CPCTC). The order of the vertices in the congruence statement indicates the correspondences.

Step2: Identify corresponding parts

In $\triangle MTD\cong\triangle SLG$, $M$ corresponds to $S$, $T$ corresponds to $L$, and $D$ corresponds to $G$.

Step3: Check each option

• For $\overline{MT}\cong\overline{GL}$, $MT$ and $GL$ are not corresponding sides.
• For $\overline{TD}\cong\overline{SG}$, $TD$ and $SG$ are corresponding sides.
• For $\angle M\cong\angle G$, $\angle M$ and $\angle G$ are not corresponding angles.
• For $\angle T\cong\angle L$, $\angle T$ and $\angle L$ are corresponding angles.

Answer:

$\overline{TD}\cong\overline{SG}$ and $\angle T\cong\angle L$ are true statements. But if we have to choose one from the given options, the answer is $\overline{TD}\cong\overline{SG}$