Question

triangle ghj is rotated 90° about point x, resulting in triangle str. which congruency statement is true?
o tr ≅ gj
o ∠s ≅ ∠h
o ts ≅ hg
o ∠r ≅ ∠g

Explanation:

Step1: Understand the rotation property

When a figure is rotated, the pre - image and the image are congruent. So, \(\triangle GHJ\cong\triangle STR\).

Step2: Analyze the congruent parts

For congruent triangles \(\triangle GHJ\) and \(\triangle STR\), the corresponding sides and angles are congruent.

• Corresponding sides: \(GH\) corresponds to \(ST\), \(HJ\) corresponds to \(TR\), \(GJ\) corresponds to \(SR\).
• Corresponding angles: \(\angle G\) corresponds to \(\angle S\), \(\angle H\) corresponds to \(\angle T\), \(\angle J\) corresponds to \(\angle R\).

Step3: Check each option

• Option 1: \(\overline{TR}\) corresponds to \(\overline{HJ}\), not \(\overline{GJ}\). So, \(\overline{TR}

ot\cong\overline{GJ}\).

• Option 2: \(\angle S\) corresponds to \(\angle G\), not \(\angle H\). So, \(\angle S

ot\cong\angle H\).

• Option 3: Since \(GH\) corresponds to \(ST\), by the property of congruent triangles (CPCTC - Corresponding Parts of Congruent Triangles are Congruent), \(\overline{TS}\cong\overline{HG}\).
• Option 4: \(\angle R\) corresponds to \(\angle J\), not \(\angle G\). So, \(\angle R

ot\cong\angle G\).

Answer:

\(\overline{TS}\cong\overline{HG}\) (the third option)