Question

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Explanation:

Step1: Calculate $m\angle G$

Sum of angles in $\triangle GHJ$: $m\angle G = 180^\circ - 83^\circ - 57^\circ = 40^\circ$. By similarity, $m\angle S = m\angle G = 40^\circ$.

Step2: Match congruent angles

Corresponding angles of similar triangles are congruent: $\angle G$ corresponds to $\angle S$, $\angle H$ corresponds to $\angle T$, $\angle J$ corresponds to $\angle U$.

Step3: Identify similar triangles

Triangles with matching angles are similar: $\triangle GHJ$ corresponds to $\triangle STU$.

Answer:

a) $m\angle G = 40^\circ$, $m\angle S = 40^\circ$
b) $\angle G \cong \angle S$
c) $\angle H \cong \angle T$
d) $\angle J \cong \angle U$
e) $\triangle GHJ \sim \triangle STU$