What are the Similarity Criteria? Exploring the Fundamentals of Shape Proportions in Geometry
- For triangles, if two triangles are similar, then their corresponding angles are equal, and their corresponding sides are in proportion.
Examples
Practice Questions
- Triangle GHI has sides of lengths \(7 \text{ cm}\), \(24 \text{ cm}\), and \(25 \text{ cm}\). Triangle \(JKL\) has sides of lengths \(14 \text{ cm}\), \(48 \text{ cm}\), and \(50 \text{ cm}\). Are the triangles similar?
- Triangle \(MNO\) has angles measuring \(35^\circ\), \(55^\circ\), and \(90^\circ\). Triangle \(PQR\) has angles measuring \(55^\circ\), \(90^\circ\), and \(35^\circ\). Are these triangles similar?
- Yes, triangles \(GHI\) and \(JKL\) are similar according to the SSS criterion with a scale factor of \(0.5\).
- Yes, triangles \(MNO\) and \(PQR\) are similar according to the AAA criterion.
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