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
In Fig. 17.29, suppose it is known that DE = DF. Then, is ΔABC isosceles? Why or why not?
Which of the following statement is true for a rectangle?
It has two pairs of equal sides.
Which of the following statement is true for a rectangle?
Its diagonals are perpendicular and bisect each other.
Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm.
Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm then find BO and if ∠CAD =35° then find ∠ACB.
A quadrilateral whose opposite sides and all the angles are equal is a ______.
Every rectangle is a trapezium.
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
Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x if JF = 8x + 4 and EG = 24x – 8.
