1. Parallel Lines:
The lines which are coplanar and do not intersect each other are called parallel lines.
2. When two lines intersect, the pairs of opposite angles formed are congruent.
3. Types of Angles:
(i) The pairs of corresponding angles in the given figure are: ∠d,∠h; ∠a, ∠e; ∠c,∠g;∠b,∠f.
(ii) The pairs of alternate interior angles in the given figure are: ∠c, ∠e; ∠b, ∠h.
(iii) The Pairs of alternate exterior angles are: ∠d, ∠f; ∠a, ∠g.
(iv) The pairs of interior angle on the same side of the transversal are: ∠c, ∠h; ∠b, ∠e.
4. Properties of Angles:
(i) The angles in a linear pair are supplementary.
(ii) When one pair of corresponding angles is congruent, then all the remaining pairs of corresponding angles are congruent.
(iii) When one pair of alternate angles is congruent, then all the remaining pairs of alternate angles are congruent.
(iv) When one pair of interior angles on one side of the transversal is supplementary, then the other pair of interior angles is also supplementary.
(v) If two parallel lines are intersected by a transversal, the interior angles on either side of the transversal are supplementary.
(vi) The corresponding angles formed by a transversal of two parallel lines are of equal measure.
5. Angle Sum Property:
The sum of measures of all angles of a triangle is 180°
6. Parallel Lines:
(i) If the interior angles on the same side of a transversal are supplementary then the lines are parallel.
(ii) If a pair of alternate angles is congruent, then the lines are parallel.
(iii) If a pair of corresponding angles is congruent, then the lines are parallel.