Question

prove that a quadrilateral is a rectangle if and only if it's diagonal are congruent and bisect each other
​

Answer 1

Step-by-step explanation:

There are three ways to prove that a quadrilateral is a rectangle. Note that the second and third methods require that you first show (or be given) that the quadrilateral in question is a parallelogram:

• If all angles in a quadrilateral are right angles, then it’s a rectangle (reverse of the rectangle definition). (Actually, you only need to show that three angles are right angles — if they are, the fourth one is automatically a right angle as well.)

• If the diagonals of a parallelogram are congruent, then it’s a rectangle (neither the reverse of the definition nor the converse of a property).

• If a parallelogram contains a right angle, then it’s a rectangle (neither the reverse of the definition nor the converse of a property).