Question

Which of these best describes the hypotenuse-angle theorem?

a. If the hypotenuse and an acute angle of a right triangle are similar to the corresponding parts of another right triangle, then the triangles are similar

b. none of these

c. If a side and an acute angle of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

d. If the hypotenuse and an acute angle of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

Answer 1

d. if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.

Answer 2

d. If the hypotenuse and an acute angle of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

Explanation:

The hypotenuse, acute angle, and right angle form a AAS triple. When these are congruent between two right triangles, the triangles are congruent by the AAS postulate.