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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.
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