Co-interior angles between parallel lines are complementary angles

Define complementary angles.

Sum of co-interior angles between parallel lines is two right angles

Alternate interior angles between parallel lines are equal

A pair of complementary angles is

Corresponding angles between parallel lines are equal

COMPLEMENTARY ANGLES If the sum of the measures of two angles is 90^@ then the angles are called complementary angles and each is called a complement of the other.

Angle between Lines and Planes

Theorem 6.4 : If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.

Read the following statements which are taken as axioms (i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal. (ii) If a transversal intersect two parallel lines, then alternate interior angles are equal. Is this system of axioms consistent ? Justify your answer.

Theorem 6.3 : If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.