Question

prove that pair of alternate angles formed by a transversal of two lines is congruent

Answer 1

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If two parallel lines are intersected by atransversal, corresponding angles are congurent, alternate interior angles arecongruent. and alternate exteriorangles are congruent. If thetransversal is perpendicular to the parallel lines, all of the angles formedare congruent to 90° angles.

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Answer 2

Yes, the pair of alternate angles formed by the transversal lines is congruent. It is when any two lines parallel to each other are cut across by a third transversal line. The pair of angles formed on the either side of the said transversal line and the ones outside the transversal lines are alternate exterior angles and are equal.

The corresponding angles, the alternate angles or the consecutive angles are respectively congruent and hence equal to each other in pairs i.e., to say alternate interior angles would be equal or congruent to the pair of interior angles so formed.