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. 55º 35º 50º130º 80º 45º 85º 20º

These angles are NOT adjacent. 45º55º 50º 100º 35º

When 2 lines intersect, they make vertical angles. 75º 105º

Vertical angles are opposite one another. 75º 105º

Vertical angles are congruent (equal). 30º150º 30º

Supplementary angles add up to 180º. 60º120º 40º 140º Adjacent and Supplementary AnglesSupplementary Angles but not Adjacent

Complementary angles add up to 90º. 60º 30º 40º 50º Adjacent and Complementary AnglesComplementary Angles but not Adjacent

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 distance apart are ____________. parallel lines No two parallel lines intersect, no matter how far you extend them.

Definition of Parallel Lines Two lines are parallel if they are in the same plane and do not ________. intersect

In geometry, a line, line segment, or ray that intersects two or more lines at different points is called a __________ transversal l m B A is an example of a transversal. It intercepts lines l and m. Note all of the different angles formed at the points of intersection

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. l m Parallel Lines t is a transversal for l and m. t b c Nonparallel Lines r is a transversal for b and c. r

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

l m When a transversal intersects two lines, _____ angles are formed. eight These angles are given special names. 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. Consecutive Interior angles are on the same side of the transversal. Alternate Exterior angles are on the opposite sides of the transversal.

Theorem 4-1 Alternate Interior Angles If two parallel lines are cut by a transversal, then each pair of alternate interior angles is _________ congruent

Theorem 4-2 Consecutive Interior Angles If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is _____________. supplementary

Theorem 4-3 Alternate Exterior Angles If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is _________. congruent

l m t 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. Angle 1 and 5 are called __________________. corresponding angles Give three other pairs of corresponding angles that are formed:  4 and  8  3 and  7  2 and  6

Postulate 4-1 Corresponding Angles If two parallel lines are cut by a transversal, then each pair of corresponding angles are _________. congruent

Concept Summary CongruentSupplementary alternate interior alternate exterior corresponding consecutive interior Types of angle pairs formed when a transversal cuts two parallel lines.

s t c d s || t and c || d. Name all the angles that are congruent to  1. Give a reason for each answer.  3   1 corresponding angles  6   1 vertical angles  8   1 alternate exterior angles  9   1 corresponding angles  11   9   1 corresponding angles  14   1 alternate exterior angles  16   14   1 corresponding angles