A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.

Solution:

Given, the diagonal of a parallelogram bisects an angle.

We have to determine if the diagonal will also bisect the other angle.

Consider a parallelogram ABCD

Let the diagonal AC bisects ∠A

Given, ∠1 = ∠2

Since AB is parallel to CD and AC is the transversal, the alternate interior angles are equal.

So, ∠1 = ∠4 -------------------------------- (1)

Similarly, ∠2 = ∠3 ------------------------- (2)

From (1) and (2),

∠3 = ∠4

Therefore, the diagonal bisects the other angle.

✦ Try This: In a quadrilateral ABCD, the measure of the three angles A, B and C are 110°, 70° and 80° respectively. Find the measure of angle D.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 177

A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.

Summary:

A diagonal of a parallelogram bisects an angle. It also bisects the other angle.

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