Math, asked by dk3646128, 1 year ago

answer the second questiom plzz i will mark branliest

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traplord: Class???

traplord: Have a look sire your answer is ready

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Answered by traplord

Given that the diagonals AC and BD of parallelogram ABCD are equal in length .

Consider triangles ABD and ACD.

AC = BD [Given]

AB = DC [opposite sides of a parallelogram]

AD = AD [Common side]

∴ ΔABD ≅ ΔDCA [SSS congruence criterion]

∠BAD = ∠CDA [CPCT]

∠BAD + ∠CDA = 180° [Adjacent angles of a parallelogram are supplementary.]

So, ∠BAD and ∠CDA are right angles as they are congruent and supplementary.

Therefore, parallelogram ABCD is a rectangle since a parallelogram with one right interior angle is a rectangle

ishant29: 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.

Answered by praneethks

Generally in a parallelogram adjacent sides are equal lets say one side of parallelogram be a and parallel to it other side be b. As they said that diagonals are equal this means that length of diagonal formed by sides having length a is same as that formed by sides having length b. so length of diagonal is √a2+a2 =√b2+b2 which is equal to √2a=√2b. so a=b it is a square it's proven so a square is also a rectangle.

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