Question

Question is in pic
[ Please solve it ]​

Answer 1

Given that,

• AC = BD

To show that, ABCD is a rectangle if the diagonals of a parallelogram are equal

To show, ABCD is a rectangle we have to prove that one of its interior angles is right angled.

Proof,

In ΔABC and ΔBAD,

• BC = BA ( Common )

AC = AD ( Opposite sides of a parallelogram are equal )

• AC = BD ( Given )

$\sf\therefore Δ ABC ≅ ΔBAD \: [SSS \: congruency]$

∠A = ∠B [ Corresponding parts of Congruent Triangles ]

Also,

∠A+∠B = 180° ( Sum of the angles on the same side of the transversal )

$\implies \sf 2∠A = 180° \\ \\ \implies \sf∠A = 90° = ∠B$

ABCD is a rectangle.

HENCE PROVED