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Corresponding Angles of Similar Triangles

publish date: 2026/05/14 21:40:15.599066 UTC

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Given that \(\triangle PQR \sim \triangle CDE\), which three pairs of angles are congruent?

\(\angle P \cong \angle C,\; \angle Q \cong \angle D,\; \angle R \cong \angle E\)

\(\angle P \cong \angle D,\; \angle Q \cong \angle C,\; \angle R \cong \angle E\)

\(\angle P \cong \angle E,\; \angle Q \cong \angle D,\; \angle R \cong \angle C\)

\(\angle P \cong \angle C,\; \angle Q \cong \angle E,\; \angle R \cong \angle D\)

Correct Answer

\(\angle P \cong \angle C,\; \angle Q \cong \angle D,\; \angle R \cong \angle E\)

Explanation

The similarity statement \(\triangle PQR \sim \triangle CDE\) establishes the vertex correspondence: P↔C, Q↔D, R↔E. Therefore the congruent angle pairs are \(\angle P \cong \angle C\), \(\angle Q \cong \angle D\), and \(\angle R \cong \angle E\).

Reference

Mathematics for college students

Quizzes you can take where this question appears

Determine whether two triangles are similar