Provide an appropriate response.Let ?I and ?E be right angles, and suppose . Prove that the diagonals and are perpendicular.

Question

What will be an ideal response?

Answer 1

Answers will vary. A sample correct response would be as follows.

By the Pythagorean Theorem, ET² + EK² = KT² and IT² + IK² = KT². Since ET = IT and KT = KT, then EK = IK. By SSS, ?KIT ? ?KET. Let X denote the point of intersection of KT and IE. Then by SAS, , and so . It follows that both of these are 90°, and so the diagonals  and  are perpendicular.