answer the second questiom plzz i will mark branliest
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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
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.
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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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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