Question

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

(overline{lg}congoverline{td})
(angle lcongangle d)
(overline{sg}congoverline{mt})
(angle scongangle t)

Explanation:

Step1: Recall congruent - triangle properties

When $\triangle MTD\cong\triangle SLG$, corresponding sides and corresponding angles are congruent. The order of the letters in the triangle - congruence statement gives the corresponding parts. That is, $M$ corresponds to $S$, $T$ corresponds to $L$, and $D$ corresponds to $G$.

Step2: Analyze each option

• For $\overline{LG}\cong\overline{TD}$, the corresponding sides should be $\overline{LG}\cong\overline{TD}$ (correct).
• For $\angle L\cong\angle D$, the corresponding angles are $\angle L\cong\angle T$, not $\angle L\cong\angle D$.
• For $\overline{SG}\cong\overline{MT}$, the corresponding sides are $\overline{SG}\cong\overline{MD}$, not $\overline{SG}\cong\overline{MT}$.
• For $\angle S\cong\angle T$, the corresponding angles are $\angle S\cong\angle M$, not $\angle S\cong\angle T$.

Answer:

$\overline{LG}\cong\overline{TD}$