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Parallel Lines and Transversals You will learn to identify the relationships among pairs of interior and exterior angles formed by two parallel lines and a transversal. Parallel Lines and Transversals In geometry, a line, line segment, or ray that intersects two or more lines at transversal different points is called a __________ A 2 1 4 5 8 6 7 3 l m B AB is an example of a transversal. It intercepts lines l and m. Note all of the different angles formed at the points of intersection. Parallel Lines and Transversals Definition of Transversal In a plane, a line is a transversal iff it intersects two or more Lines, each at a different point. The lines cut by a transversal may or may not be parallel. Parallel Lines Nonparallel Lines l 1 2 4 3 lm t 1 2 4 3 m 5 6 8 7 c 5 6 8 7 b || c t is a transversal for l and m. b r r is a transversal for b and c. Parallel Lines and Transversals Two lines divide the plane into three regions. The region between the lines is referred to as the interior. The two regions not between the lines is referred to as the exterior. Exterior Interior Exterior Parallel Lines and Transversals eight angles are formed. When a transversal intersects two lines, _____ These angles are given special names. l 1 2 4 3 m 5 6 8 7 t Interior angles lie between the two lines. Exterior angles lie outside the two lines. Alternate Interior angles are on the opposite sides of the transversal. Alternate Exterior angles are on the opposite sides of the transversal. Consectutive Interior angles are on the same side of the transversal. Parallel Lines and Transversals Theorem 4-1 If two parallel lines are cut by a transversal, then each pair of congruent Alternate Alternate interior angles is _________. Interior Angles 1 2 4 3 5 6 8 7 4 6 3 5 Parallel Lines and Transversals Theorem 4-2 If two parallel lines are cut by a transversal, then each pair of supplementary Consecutive consecutive interior angles is _____________. Interior Angles 1 2 4 3 5 6 8 7 4 5 180 3 6 180 Parallel Lines and Transversals Theorem 4-3 If two parallel lines are cut by a transversal, then each pair of congruent Alternate alternate exterior angles is _________. Exterior Angles 1 2 4 3 5 6 8 7 1 7 2 8 Transversals and Corresponding Angles When a transversal crosses two lines, the intersection creates a number of angles that are related to each other. Note <1 and <5 below. Although one is an exterior angle and the other is an interior angle, both lie on the same side of the transversal. corresponding angles Angle 1 and 5 are called __________________. l 1 2 4 3 m 5 6 8 7 t Give three other pairs of corresponding angles that are formed: <4 and <8 <3 and <7 <2 and <6 Transversals and Corresponding Angles Postulate 4-1 If two parallel lines are cut by a transversal, then each pair of congruent Corresponding corresponding angles is _________. Angles