if the diagonals of a parallelogram are equal, then show that it is a rectanlge
Answers
Answer:
the opposite sides of an parellelogram are equal and hence it is an rectangle because the opposite sides of rectangle are equal
Step-by-step explanation:
Let ABCD be a parallelogram. To show that ABCD is a rectangle, we have to prove that one of
its interior angles is 90°
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 180°
∠ABC + ∠DCB = 180° [AB || CD]
=> ∠ABC + ∠ABC = 180°
=> 2∠ABC = 180°
=> ∠ABC = 90°
Since ABCD is a parallelogram and one of its interior angles is 90°, ABCD is a rectangle.
Hope it helps you!
Please mark me as the brainliest!