Question

if the diagonals of a quadrilateral are equal and bisect each other not at right angles prove that the quadrilateral is a rectangle

Answer 1

Question

If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Solution :

Let ABCD be a parallelogram. To show that ABCD is a rectangle, we have to prove that one of

its interior angles is 900.

In ΔABC and ΔDCB,

AB = DC (Opposite sides of a parallelogram are equal)

BC = BC (Common)

AC = DB (Given)

By SSS congruence rule,

ΔABC ≅ ΔDCB

So, ∠ABC = ∠DCB

It is known that the sum of measures of angles on the same side of traversal is 1800

∠ABC + ∠DCB = 1800 [AB || CD]

=> ∠ABC + ∠ABC = 1800

=> 2∠ABC = 1800

=> ∠ABC = 900

Since ABCD is a parallelogram and one of its interior angles is 900, ABCD is a rectangle.

Answer 2

Step-by-step explanation:

See image