4-2: Parallel Lines and Transversals

4-2: Parallel Lines and TransversalsTRANSVERSAL: A line, line segment, or ray

that intersects two or more lines at different points.

4-2: Parallel Lines and Transversals When a transversal intersects two lines, eight angles are

formed. INTERIOR ANGLES: Angles between

the two lines3, 4, 5, 6

ALTERNATE INTERIOR ANGLES:pairs of interior angles that are on opposite sides of the transversal3 & 5, 4 & 6

CONSECUTIVE INTERIOR ANGLES: pairs of interior angles that are on the same side of the transversal4 & 5, 3 & 6

EXTERIOR ANGLES: Angles that lie outside the two lines1, 2, 7, 8

ALTERNATE EXTERIOR ANGLES: pairs of exterior angles that are on opposite sides of the transversal1 & 7, 2 & 8

4-2: Parallel Lines and TransversalsIdentify each pair of angles

as alternate interior, alternate exterior, consecutive interior, or vertical2 & 8

1 & 6

2 & 4

4 & 6

Alternate exterior

Consecutive interior

Vertical

Alternate interior

4-2: Parallel Lines and TransversalsIf 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)

4-2: Parallel Lines and TransversalsIn the figure, p || q, and

r is a transversal. If m5 = 28, find:m8

m1

m2

m3

m4

28

152

28

28

152

4-2: Parallel Lines and TransversalsAssignment

Worksheet #4-2