2. If the diagonals of a …

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2. If the diagonals of a parallelogram are equal, show that it is a rectangle.

Posted by Mohit Solanki 4 years ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 4 years ago

□ 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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