What is a key property of similar triangles?

What is a key property of similar triangles?

• A. Only one angle is equal and sides are proportional
• B. All corresponding angles are equal and all corresponding sides are in proportion
• C. Triangles are similar only if they have equal perimeters
• D. Similar triangles have equal areas

Answer: (B)

Similar triangles are the same shape, just different sizes. The defining property is that every angle in one triangle matches the corresponding angle in the other, and the corresponding sides are in a constant proportion to each other. That constant is a scale factor, so you can stretch or shrink one triangle to becomes the other, multiplying all three sides by the same number and keeping all three angles the same. Seeing only one angle match isn’t enough to guarantee similarity, because the other angles would need to match as well, and the sides must stay in the same ratio. Perimeters can be equal in non-similar cases, and areas can differ even when triangles are similar (areas scale with the square of the linear scale factor), so those ideas don’t define similarity.

Similar triangles are the same shape, just different sizes. The defining property is that every angle in one triangle matches the corresponding angle in the other, and the corresponding sides are in a constant proportion to each other. That constant is a scale factor, so you can stretch or shrink one triangle to becomes the other, multiplying all three sides by the same number and keeping all three angles the same.

Seeing only one angle match isn’t enough to guarantee similarity, because the other angles would need to match as well, and the sides must stay in the same ratio. Perimeters can be equal in non-similar cases, and areas can differ even when triangles are similar (areas scale with the square of the linear scale factor), so those ideas don’t define similarity.