Question

7. If the diagonals of a parallelogram are equal, then show that it is rectangle​

Answer 1

Answer:

according to series of quadrilateral

in parallelogram opposite sides are equal but diagonal not equal then it rectangle opp equal , diagonal also equal

Answer 2

Step-by-step explanation:

□ 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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