Question

In the diagram below, BC = QR=1, AC = PR=y, and triangle PQR is a right triangle. Use the drop-down menus to complete the proof that if the equation x2 + y2 = z2 is true of the side lengths in triangle ABC, then triangle ABC must be a right triangle.

Answer 1

In order to complete the sentence correctly, the first option for the drop-down menu should be z² = PQ² and z = PQ, because we can use the Pythagorean theorem in the right triangle and the triangles are congruent.

Then, for the second drop-down menu, we want to show that the first triangle is also a right triangle, so the option is C = R, this way we have a right angle in the vertex C.