Question

If the adjacent angles of a parallelogram are equal then is the parallelogram a rectangle? Justify ur answer bye arguments.​

Answer 1

Answer:

Given that the diagonals AC and BD of parallelogram ABCD are congruent. 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.

Step-by-step explanation:

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Answer 2

Answer:

According to the properties of a parallelogram it's adjacent angles are supplementary i.e their sum is equal to 180 degree. These angles can be equal when they are 90 each and when they will be 90 each it would become a rectangle and not a parallelogram.

Also according to the properties of rectangle it's adjacent angles are equal.

Therefore the answer is rectangle.

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