Similar triangles have which properties?

Similar triangles have which properties?

• A. Equal angles and proportional sides
• B. Equal angles and equal sides
• C. Proportional angles and equal sides
• D. Equal sides and same size

Answer: (A)

Similar triangles share the same shape, which means their corresponding angles are equal and their corresponding sides are in the same ratio. That ratio can be any positive number, so the triangles can be different sizes but still have the same angles. So, equal angles combined with proportional sides is the defining idea of similarity. Having equal angles and equal sides would make the triangles congruent, not just similar, since congruent triangles are identical in size and shape. The idea of proportional angles doesn’t apply, because angles aren’t measured by a scale—they’re either equal or not.

Similar triangles share the same shape, which means their corresponding angles are equal and their corresponding sides are in the same ratio. That ratio can be any positive number, so the triangles can be different sizes but still have the same angles. So, equal angles combined with proportional sides is the defining idea of similarity.

Having equal angles and equal sides would make the triangles congruent, not just similar, since congruent triangles are identical in size and shape. The idea of proportional angles doesn’t apply, because angles aren’t measured by a scale—they’re either equal or not.