Question

if the diagonal of paralllelogram is equal then show that it is a rectangle ​

Answer 1

Answer:

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Step-by-step explanation:

I don't know

Answer 2

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Given

• ABCD is a parallelogram
• AB = CD, BC = AD
• AC = BD

To Prove

• ABCD is a rectangle
• AB = CD, AC = BD
• ∠A = ∠B = ∠C = ∠D = 90°

Proof

In △ABC and △DAB

AD = BC [ opp. sides of a llgm are equal ]

AB = BA [ Common ]

AC = BD [ Given ]

△ABC ≅ △DAB [ by SSS congruence rule ]

∠A = ∠B [ by CPCT ] -------eq.1

Since ABCD is a ||gm and AB is a transversal.

➞ ∠A + ∠B = 180° [ Co-interior Angle ]

➞ ∠A + ∠A = 180° [ from eq. 1 ]

➞ 2∠A = 180°

➞ ∠A = 180° / 2

➞ ∠A = 90°

Since opposite angles of parallelogram are equal

Therefore, ∠A = ∠B = ∠C = ∠D = 90°

Hence, ABCD is a rectangle.