Question

If the diagonals of a parallelogram are equal then show that it is a rectangle by linear pair

Answer 1

lets say, ABCD is a parallelogram



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.

Answer 2

Answer:

Step-by-step explanation:

In parallelogjam ABCD

angle ABD = angle BDC (AC=BD (GIVEN))

angle ACD+angle BDC =180 °

2angleACD =180°

angle ACD = angle BDC = 90°

angle ACD=90°

So,Parrallelogram ABCD is a rectangle