Question

1. $\angle s \cong \angle i, \angle g \cong \angle a$

$t$ is the midpoint of $si$.
is $\overline{sg} \cong \overline{ia}$? (h)

Explanation:

Step1: Identify Given Information

We know that $\angle S \cong \angle I$, $\angle G \cong \angle A$, and $T$ is the midpoint of $\overline{SI}$, so $ST = IT$.

Step2: Apply ASA Congruence Criterion

In $\triangle STG$ and $\triangle ITA$:

• $\angle S \cong \angle I$ (Given)
• $ST = IT$ (Midpoint definition)
• $\angle G \cong \angle A$ (Given)

By the Angle - Side - Angle (ASA) congruence postulate, $\triangle STG \cong \triangle ITA$.

Step3: Corresponding Parts of Congruent Triangles

Since $\triangle STG \cong \triangle ITA$, their corresponding sides are congruent. The side $SG$ in $\triangle STG$ corresponds to side $IA$ in $\triangle ITA$. So, $SG \cong IA$.

Answer:

Yes, $SG \cong IA$ because $\triangle STG \cong \triangle ITA$ by ASA congruence, so their corresponding sides are congruent.