Math, asked by mahee3, 1 year ago

if the diagonals are a parallelogram are equal , then show it is a rectangle

Answers

Answered by sonisrishti2002
2
Let ABCD be that parallelogram
Then AC=BD.
Now in ABD and BCD,
BD=BD
AB=CD
AD=BC
So, ABD is congruent to BCD
=> angle A = angle C
We know that the sum of opposite angles of a parallelogram is 180.
So, angle A + angle C= 180
=> 2angle A =180
So, angleA=90.
Since a parallelogram with opposite sides equal and all angles 90 degree, is a rectangle.
Answered by shreya204
1

Let ABCD be a parallelogram. To show that ABCD is a rectangle, we have to prove that one of its interior angles is 90º.

In ΔABC and ΔDCB,

AB = DC (Opposite sides of a parallelogram are equal)

BC = BC (Common)

AC = DB (Given)

∴ ΔABC ≅ ΔDCB (By SSS Congruence rule)

⇒ ∠ABC = ∠DCB

It is known that the sum of the measures of angles on the same side of transversal is 180º.

∠ABC + ∠DCB = 180º (AB || CD)

⇒ ∠ABC + ∠ABC = 180º

⇒ 2∠ABC = 180º

⇒ ∠ABC = 90º

Since ABCD is a parallelogram and one of its interior angles is 90º, ABCD is a rectangle.

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