Question

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

Explanation:

Step1: Recall rotation property

A rotation is a rigid - motion transformation. Rigid - motion transformations preserve side lengths and angle measures. When \(\triangle GHJ\) is rotated 90° about point \(X\) to get \(\triangle STR\), the corresponding parts of the two triangles are congruent. The order of the vertices in the congruence statement matters. If \(\triangle GHJ\cong\triangle STR\), then \(G\) corresponds to \(S\), \(H\) corresponds to \(T\), and \(J\) corresponds to \(R\).

Step2: Check each option

• For \(\overline{TR}\cong\overline{GJ}\), the correct correspondence is \(\overline{TR}\cong\overline{HJ}\), so this is false.
• For \(\angle S\cong\angle H\), the correct correspondence is \(\angle S\cong\angle G\), so this is false.
• For \(\overline{TS}\cong\overline{HG}\), since \(T\) corresponds to \(H\) and \(S\) corresponds to \(G\), \(\overline{TS}\cong\overline{HG}\) is true.
• For \(\angle R\cong\angle G\), the correct correspondence is \(\angle R\cong\angle J\), so this is false.

Answer:

\(\overline{TS}\cong\overline{HG}\)