Which is the hypotenuse-angle theorem?

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A. 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.
B. If the hypotenuse and an obtuse angle of a right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.
C. 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 complimentary.
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 supplementary.

For heaven's sake, read the choicea and figure out what they are saying. Then choose the one that makes sense.

B. Right triangles do not have obtuse angles

C. and D. The words "complimentary" and "supplementary" refer to angles, not triangles.

We will gladly critique your thinking.

The correct answer is A. 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.

To determine this answer, you can use the Hypotenuse-Angle Theorem, also known as the Side-Angle-Side (SAS) Congruence Theorem. This theorem states that if two triangles have two pairs of corresponding sides that are congruent and the included angles are congruent, then the triangles are congruent.

In the case of the Hypotenuse-Angle Theorem, it specifically applies to right triangles. It states that 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. This means that if you have two right triangles where the hypotenuses and one of the acute angles are congruent, then the triangles are congruent.

To verify the congruence of the triangles, you would need to compare the lengths of the hypotenuses and measure the angles to ensure that they are congruent. If these conditions are met, you can conclude that the two right triangles are congruent based on the Hypotenuse-Angle Theorem.