Question

Similarity in right triangles.

10 and 14

Answer 1

To determine whether two right triangles are similar, we need to check if their corresponding angles are congruent and their corresponding sides are proportional.

Let's assume that the two triangles are ABC and DEF, where angle A is congruent to angle D, and B is congruent to E. We need to find out if the corresponding sides are proportional.

Using the Pythagorean Theorem, we can find that the length of side AC is:

AC = √(AB² + BC²)

AC = √(10² + 14²)

AC = √296

AC ≈ 17.2

Similarly, we can find that the length of side DF is:

DF = √(DE² + EF²)

DF = √(10² + 14²)

DF = √296

DF ≈ 17.2

Therefore, the two triangles are similar because their corresponding angles are congruent and their corresponding sides are proportional.