Question

2. If the diagonals of a parallelogram are equal, then show that it is a rectangle​

Answer 1

Answer:

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Answer 2

Question :-

• If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Given :-

• In parallelogram ABCD, AC = BD

To prove :-

• Parallelogram ABCD is rectangle.

Proof :-

In $\triangle$ ABC and $\triangle$ BDA

AC = BD ( Given )

AB = BA ( Common )

BC = AD ( Opposite side of

parallelogram are eqal )

$\triangle$ ACB $\cong$ $\triangle$ BDA ( SSS Cong rule )

$\therefore$ $\angle$ ABC = $\angle$ BDA ------ (1) CPCT

AD $\parallel$ ( Opposite side of parallelogram ABCD )

AD $\parallel$ BC and the transversal AB intersect them.

$\therefore$ $\angle$ BAD + $\angle$ ABC = 180°--------(2) [sum of

consecutive interior angel on

the same side of the

transversal is 180°)

From eq 1st and 2nd

$\angle$ BAD = $\angle$ ABC = 90°

$\therefore$ $\angle$ A = 90° and $\angle$ C = 90°

$\therefore$ Parallelogram ABCD is a rectangle.

Hence Proved !!