Proof saves nine

Question

Elena wants to prove that a quadrilateral with 4 right angles must have congruent opposite sides. Explain to Elena how she can use the fact that all rectangles are parallelograms in her proof.

Answer 1

The opposite sides are PARALLEL because of the inverse alternating angles theorem, which states

that if the alternate interior/external angles are congruent then the lines are parallel.

Quadrilateral ABCD, A at top left going clockwise...

Draws diagonal AC. Then angle BAC = angle DCA by parallel lines.

AC=CA by reflexive.

So right triangles ABC and CDA are congruent ASA, LA, and various other theorems..

opposite sides are congruent by CPCTC

Answer 2

Use same side interior angles.