If triangles \( \triangle PQR \) and \( \triangle JKL \) are similar (denoted as \( \triangle PQR \sim \triangle JKL \)), then the following statements are correct:
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Corresponding Angles are Equal: The angles of the triangles that correspond to each other are equal. That is:
- \( \angle P = \angle J \)
- \( \angle Q = \angle K \)
- \( \angle R = \angle L \)
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Corresponding Sides are Proportional: The lengths of the sides of the triangles are in proportion. For corresponding sides, this means:
- \( \frac{PQ}{JK} = \frac{QR}{KL} = \frac{PR}{JL} \)
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Same Shape: The triangles retain the same shape but may differ in size.
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Scale Factor: There exists a scale factor \( k \) such that:
- \( PQ = k \cdot JK \)
- \( QR = k \cdot KL \)
- \( PR = k \cdot JL \)
These properties are fundamental to the concept of similar triangles. If you have specific statements in mind, please share them, and I can verify which ones are correct.