In similar triangles, what is true about the ratio of corresponding sides?

In similar triangles, what is true about the ratio of corresponding sides?

• A. Constant ratio
• B. Always equal in length
• C. Varies with each pair
• D. Opposite to each other

Answer: (A)

When two triangles are similar, they have the same shape but can be different sizes. In that case, every pair of corresponding sides grows or shrinks by the same factor. There’s a scale factor k such that each side in one triangle is k times the length of the corresponding side in the other: a' = k a, b' = k b, c' = k c. This means the ratio of any two corresponding sides is constant across all three pairs. It’s not that the sides are equal in length unless the triangles are the same size (k = 1). It also doesn’t vary from pair to pair or relate to any notion of being opposite.

When two triangles are similar, they have the same shape but can be different sizes. In that case, every pair of corresponding sides grows or shrinks by the same factor. There’s a scale factor k such that each side in one triangle is k times the length of the corresponding side in the other: a' = k a, b' = k b, c' = k c. This means the ratio of any two corresponding sides is constant across all three pairs. It’s not that the sides are equal in length unless the triangles are the same size (k = 1). It also doesn’t vary from pair to pair or relate to any notion of being opposite.