Question

If the diagonal of a parellelogram are equal, then show that it is a rectangle​

Answer 1

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□ ABCD is a parallelogram

consider Δ ACD and Δ ABD

AC = BD .... (given)

AB = DC .... (opposite sides of parallelogram)

AD = AD .... (common side)

∴Δ ACD ≅Δ ABD (sss test of congruence)

∠ BAD = ∠ CDA .... (cpct)

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

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

Therefor, □ ABCD is a rectangle since a 

parallelogram with one right interior angle is a rectangle.

Answer 2

Step-by-step explanation:

• In a Quadrilateral Abcd, ∠B = 90°, Ad2 = Ab2 + Bc2 + Cd2, Prove that ∠Acd = 90°. - Mathematics. In a quadrilateral ABCD, ∠B = 90°, AD2 = AB2 + BC2 + CD2, prove that ∠ACD = 90