Question

Which information is needed to show that a parallelogram is a rectangle? question 5 options: the diagonals bisect each other. the diagonals are congruent. the diagonals are congruent and perpendicular. the diagonals bisect each other and are perpendicular?

Answer 1

The diagonals are congruent. Since all rectangles are also parallelograms, let's check which option provides that little extra kick to make a parallelogram a rectangle. The diagonals bisect each other. * This would be wrong. The perpendiculars bisect each other in all parallelogram. So this won't make a parallelogram a rectangle and this is a bad choice. The diagonals are congruent. * This would work. Since the diagonals are congruent, they along with the parallelogram will form 4 congruent triangles. And the only way all 4 triangles can be congruent is if they're all right triangles. So this is the correct choice. The diagonals are congruent and perpendicular. * Sorry, the diagonals in a rectangle are generally not perpendicular. The only time that they are perpendicular is if the rectangle is also a square. So this is a bad choice. The diagonals bisect each other and are perpendicular * This is only true if the rectangle is a square. So it's over specific and therefore a bad choice.