Question

triangle ghj is rotated 90° about point x, resulting in triangle str. which congruency statement is true?
○ (overline{tr}congoverline{gj})
○ (angle scongangle h)
○ (overline{ts}congoverline{hg})
○ (angle rcongangle g)

Explanation:

Step1: Understand rotation property

Rotation is a rigid transformation. So, \(\triangle GHJ\cong\triangle STR\). Corresponding parts of congruent triangles are congruent.

Step2: Identify corresponding parts

• For \(\overline{TR}\) and \(\overline{GJ}\): \(\overline{TR}\) corresponds to \(\overline{GJ}\) (wrong as \(TR\) corresponds to \(GJ\) but let's check other options).
• For \(\angle S\) and \(\angle H\): \(\angle S\) corresponds to \(\angle G\) (not \(\angle H\)).
• For \(\overline{TS}\) and \(\overline{HG}\): Since \(\triangle GHJ\cong\triangle STR\), \(TS\) corresponds to \(HG\) (by CPCTC - Corresponding Parts of Congruent Triangles are Congruent).
• For \(\angle R\) and \(\angle G\): \(\angle R\) corresponds to \(\angle J\) (not \(\angle G\)).

Answer:

\(\overline{TS}\cong\overline{HG}\) (i.e., the option \(\overline{TS}\cong\overline{HG}\) is correct)