Let and be two parallel lines and be a transversal. Show that the angle bisectors of a pair of two internal angles on the same side of the transversal are perpendicular to each other.

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Solution

Let MO and NO bisect internal angles DMN and MNB respectively.

Angles DMN and MNB are interior angles.

Consider triangle MNO.

Hence, the bisectors intersect at right angle.

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Let and be two parallel lines and be a transversal. Show that the angle bisectors of a pair of two internal angles on the same side of the transversal are perpendicular to each other.

Let MO and NO bisect internal angles DMN and MNB respectively. Angles DMN and MNB are interior angles. Consider triangle MNO. Hence, the bisectors intersect at right angle.

Let MO and NO bisect internal angles DMN and MNB respectively.

Angles DMN and MNB are interior angles.

Consider triangle MNO.

Hence, the bisectors intersect at right angle.