Question

if the diagonlas of a parallelogram are eual, then show it is a rectangle​

Answer 1

$\textsf{\underline{\large{Question:}}}$

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

$\huge\underline\green{\tt Solution:}$

$\sf\blue{\underline{Given:}}$

• ABCD is a parallelogram.
• Diagonals are equal. So, AB = DC & AD = BC

$\sf\blue{\underline{To\:prove:}}$

• ABCD is a rectangle

$\huge\underline{\tt Proof:- }$

In triangle ABC and DCB,

AB = DC  ( given )

BC = CB  ( common )

AC = BD  ( given )

∴ Δ ABC ≅ Δ DCB ( by SSS rule )

Also,

∠ ABC = ∠ DCB ( by CPCT )

Now,

∠ABC + ∠DCB = 180° ( Interior angles on the same side of the transversal. )

⇒ ∠ABC + ∠ABC = 180° ( ∠ABC = ∠DCB )

⇒ 2∠ABC = 180°

⇒ ∠ABC = $\dfrac{180}{2}$

∴ ∠ABC = 90°

Here, One angle of the parallelogram is 90°. It's a prperty of a rectangle.

Hence,

The given parallelogram is rectangle!