Advertisements
Advertisements
प्रश्न
If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.
Advertisements
उत्तर
Given : //gm ABCD in which AC = BD
To Prove: ABCD is rectangle.
Proof : In ∆ABC and ∆ABD
AB = AB (Common)
AC = BD (Given)
BC = AD (opposite sides of ||gm)
∆ABC = ∆ABD (S.S.S. Rule)
∠A = ∠B
But AD // BC (opp. sides of ||gm are ||)
∠A + ∠B = 180°
∠A = ∠B = 90°
Similarly ∠D = ∠C = 90°
Hence ABCD is a rectangle.
APPEARS IN
संबंधित प्रश्न
Explain why a rectangle is a convex quadrilateral.
The shorter side of a parallelogram is 4.8 cm and the longer side is half as much again as the shorter side. Find the perimeter of the parallelogram.
Which of the following statement are true for a square?
It has all its sides of equal length.
The sides of a rectangle are in the ratio 2 : 3, and its perimeter is 20 cm. Draw the rectangle.
The sides of a rectangle are in the ratio 4 : 5. Find its sides if the perimeter is 90 cm.
Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm.
Prove that quadrilateral formed by the intersection of angle bisectors of all angles of a parallelogram is a rectangle.
Adjacent sides of a rectangle are 7 cm and 24 cm. Find the length of its diagonal.
A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and ∠PQR = 90°. Then PQRS is a ______.
Rectangle is a regular quadrilateral.
