Answer to Question #148314 in Geometry for J

Question

Prove that if two lines in same plane are cut by a transversal then the two lines are parallel if and only if a pair of interior angles on the same side of the transversal are supplementary.

Answer 1

Given: AB||CD, transversal line, l.

To prove: Sum of interior angles, 1 and 2 is 180^o.

Prove: Angle 1 + exterior angle of 1 =180^o(sum of angles on a straight line)---------(1)

Exterior angle of 1 = Angle 2(corresponding angles of parallel lines are equal)------------(2)

Substituting (2) for exterior angle of 1 into (1).

Angle 1 = $180^{\circ}$- Angle 2.

Therefore, Angle 1 + Angle 2 = 180^o.