1. 4-2: Parallel Lines and Transversals

2. T RANSVERSAL : A line, line segment, or ray that intersects two or more lines at different points.

3. 4-2: Parallel Lines and Transversals When a transversal intersects two lines, eight angles are formed. I NTERIOR A NGLES : Angles between the two lines 3, 4, 5, 6 A LTERNATE I NTERIOR A NGLES : pairs of interior angles that are on opposite sides of the transversal 3 & 5, 4 & 6 C ONSECUTIVE I NTERIOR A NGLES : pairs of interior angles that are on the same side of the transversal 4 & 5, 3 & 6 E XTERIOR A NGLES : Angles that lie outside the two lines 1, 2, 7, 8 A LTERNATE EXTERIOR A NGLES : pairs of exterior angles that are on opposite sides of the transversal 1 & 7, 2 & 8

4. 4-2: Parallel Lines and Transversals Identify each pair of angles as alternate interior, alternate exterior, consecutive interior, or vertical 2 & 8 1 & 6 2 & 4 4 & 6 Alternate exterior Consecutive interior Vertical Alternate interior

5. 4-2: Parallel Lines and Transversals If two parallel lines are cut by a transversal, then… THEOREM 4-1: alternate interior angles are congruent (3  5, 4  6) THEOREM 4-2: consecutive interior angles are supplementary (3 + 6 = 180˚, 4 + 5 = 180˚) THEOREM 4-3: alternate exterior angles are congruent (1  7, 2  8)

6. 4-2: Parallel Lines and Transversals In the figure, p || q, and r is a transversal. If m5 = 28, find: m8 m1 m2 m3 m4 28 152 28 28 152

7. 4-2: Parallel Lines and Transversals Assignment Worksheet #4-2