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Complimentary Angles, Supplementary Angles, and Parallel Lines Adjacent angles are “side by side” and share a common ray. 45º 15º These are examples of adjacent angles. 80º 35º 45º 55º 85º 130º 20º 50º These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º When 2 lines intersect, they make vertical angles. 75º 105º 105º 75º Vertical angles are opposite one another. 75º 105º 105º 75º Vertical angles are congruent (equal). 150º 30º 30º 150º Supplementary angles add up to 180º. 40º 120º 60º Adjacent and Supplementary Angles 140º Supplementary Angles but not Adjacent Complementary angles add up to 90º. 30º 40º 60º Adjacent and Complementary Angles 50º Complementary Angles but not Adjacent Parallel Lines and Planes You will learn to describe relationships among lines, parts of lines, and planes. In geometry, two lines in a plane that are always the same parallel lines distance apart are ____________. No two parallel lines intersect, no matter how far you extend them. Parallel Lines and Planes Definition of Parallel Lines Two lines are parallel if they are in the same plane and intersect do not ________. 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 if 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. Consecutive 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 are _________. Angles Transversals and Corresponding Angles Types of angle pairs formed when a transversal cuts two parallel lines. Concept Summary Congruent Supplementary alternate interior consecutive interior alternate exterior corresponding Transversals and Corresponding Angles s s || t and c || d. Name all the angles that are congruent to 1. Give a reason for each answer. 1 2 5 6 9 10 13 14 3 1 corresponding angles 6 1 vertical angles 8 1 alternate exterior angles 9 1 corresponding angles 14 1 alternate exterior angles 11 9 1 corresponding angles 16 14 1 corresponding angles t 3 7 11 12 15 16 c 4 8 d