Question -
Answer -
Given that,
AC = BD
To show that, ABCD is a rectangle if the diagonals of aparallelogram are equal
To show ABCD is a rectangle we have to prove that one of itsinterior angles is right angled.
Proof,
In ΔABC and ΔBAD,
BC = BA (Common)
AC = AD (Opposite sides of a parallelogram are equal)
AC = BD (Given)
Therefore, ΔABC ≅ ΔBAD[SSS congruency]
∠A = ∠B [Corresponding parts of CongruentTriangles]
also,
∠A+∠B = 180° (Sum of the angles on the sameside of the transversal)
⇒ 2∠A = 180°
⇒ ∠A = 90° = ∠B
, ABCD is a rectangle.
Hence Proved.