Question

If the adjacent angles of a parallelogram are equal then is the parallelogram
a rectangle ? Justify your answer by 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.