Advertisements
Advertisements
Question
If the diagonals of a parallelogram are of equal lengths, the parallelogram is a rectangle. Prove it.
Advertisements
Solution
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
RELATED QUESTIONS
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.
Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 10)°. Find the angles of the parallelogram.
In a parallelogram ABCD, the diagonals bisect each other at O. If ∠ABC = 30°, ∠BDC = 10° and ∠CAB = 70°. Find:
∠DAB, ∠ADC, ∠BCD, ∠AOD, ∠DOC, ∠BOC, ∠AOB, ∠ACD, ∠CAB, ∠ADB, ∠ACB, ∠DBC and ∠DBA.
In the following figure, ABCD and AEFG are parallelograms. If ∠C = 55°, what is the measure of ∠F?
Fill in the blank of the following, so as to make the statement true:
A square is a rectangle in which .....
Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm.
Draw a rectangle ABCD such that l(AB) = 6.0 cm and l (BC) = 4.5 cm.
If diagonals of a quadrilateral are equal, it must be a rectangle.
Every trapezium is a rectangle.
A playground is in the form of a rectangle ATEF. Two players are standing at the points F and B where EF = EB. Find the values of x and y.
