Question

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Answer 1

Answer:

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Step-by-step explanation:

ANSWER

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