Question

if the diagonal of a parallelogram are equal,than show that it is a rectangle​

Answer 1

Step-by-step explanation:

Answer. Given that the diagonals AC and BD of parallelogram ABCD are equal in length . ... Therefore, parallelogram ABCD is a rectangle since a parallelogram with one right

Answer 2

Answer:

Step-by-step explanation:

Let ABCD be the parallelogram

Its given that diagonals are equal

ie AC = BD

To Prove:- ABCD is a rectangle

Proof:-

Rectangle is a parallelogram with one angle is 90 degrees

We prove that one of its angle is 90 degrees

Consider triangles ABC and DCB.

AB = DC

AC = DB

∴ ΔABC ≅ ΔDCB [SSS congruence criterion]

∠ABC = ∠DCB [CPCT]  -----EQN 1

Now AB ║ DC

And BC is transversal

∠B + ∠C = 180°

From Equation ∠B = ∠C

∠B + ∠B = 180°

2∠B = 180°

∠B = 180°/2

90°

Therefore, parallelogram ABCD is a rectangle since a parallelogram with one right interior angle is a rectangle.