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
Which of the following statement is true for a rectangle?
It has all its sides of equal length.
Which of the following statement is true for a rectangle?
Its diagonals bisect each other.
Which of the following statement is true for a rectangle?
All rectangles are squares.
Which of the following statement true for a square?
Its diagonals are equal to its sides.
Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.
If diagonal of a rectangle is 26 cm and one side is 24 cm, find the other side.
For which of the following figures, all angles are equal?
All squares are rectangles.
PQRS is a rectangle. The perpendicular ST from S on PR divides ∠S in the ratio 2:3. Find ∠TPQ.
In rectangle READ, find ∠EAR, ∠RAD and ∠ROD
