Question

Lorie correctly determines that for the triangle below, the statement ANMO ~ ATSR and the statement ANMO ~ ATRS both describe the relationship between the two triangles. Which best describes why both similarity statements are correct?

A. Corresponding angles are congruent.
B. All angles are equal in both triangles.
C. Proportions of corresponding sides are equal.
D. The triangles share a common angle.

Answer 1

The triangles are similar because the ratios of corresponding sides are equal. While corresponding angles being congruent is true, it is the proportionality of sides, as stated in option C, that ensures the similarity of the triangles.Thus the correct option is: C. Proportions of corresponding sides are equal.

Step-by-step explanation:

The correct choice is C, "Proportions of corresponding sides are equal." This is because the concept of similarity between two triangles is primarily based on the equality of corresponding angles and the proportionality of corresponding sides.

In similar triangles, corresponding angles are indeed congruent, but this alone does not make the triangles similar. The key property is the ratio of corresponding sides being equal. Therefore, choices A and B are not sufficient explanations for the similarity of the triangles.

Option D, "The triangles share a common angle," is a bit misleading. While it is true that similar triangles do share at least one congruent angle, this alone does not guarantee similarity; the proportionality of corresponding sides is crucial.

To elaborate, in similar triangles, the ratios of corresponding sides are constant. This means that if we take any pair of sides from the first triangle and the corresponding pair from the second triangle, their ratios will be the same. This concept is fundamental to understanding and establishing similarity between geometric figures.Thus the correct option is: C. Proportions of corresponding sides are equal.