Slide 1 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Lines and Angles Section9.1

Slide 2 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Identifying Lines, Line Segments. Rays, and Angles Space extends in all directions indefinitely. A Plane is a flat surface that extends indefinitely.

Slide 3 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Identifying Lines, Line Segments. Rays, and Angles A point has no length, no width, and no height, but it does have a location. P Point P A line is set of points extending indefinitely in two directions. Line AB or AB A B

Slide 4 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Identifying Lines, Line Segments. Rays, and Angles DefinitionExample Line Segment - A piece of a line with two endpoints. Ray - A part of a line with one endpoint. Angle - Made up of two rays that share the same endpoint. Vertex - The common endpoint of an angle. A B Line segment AB or A B Ray AB or A B C Vertex

Slide 5 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example Identify each figure as a line, a ray, a line segment, or an angle. Then name the figure using the given point. a. b. c. F G N P R S

Slide 6 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Classifying Angles as Acute, Right, Obtuse, or Straight DefinitionExample Degrees - used to measure angles, symbolized by a small raised circle . Straight angle - an angle that measures 180 . Right angle - an angle that measures 90 .

Slide 7 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Classifying Angles as Acute, Right, Obtuse, or Straight DefinitionExample Acute Angle - an angle whose measure is between 0  and 90 . Obtuse Angle - an angle that measures between 90  and 180 .

Slide 8 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example Classify each angle as acute, right, obtuse, or straight. a.b. c.d. obtuse acute straight right

Slide 9 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Identifying Complementary and Supplementary Angles DefinitionExample Complementary Angles – two angles that have a sum of 90 . Supplementary Angles – two angles that have a sum of 180 .

Slide 10 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example Find the complement of a 62  angle. Two angles that have a sum of 90  are complementary.

Slide 11 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example Find the supplement of a 121  angle. Two angles that have a sum of 180  are supplementary.

Slide 12 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Finding Measures of Angles Two lines in a place can either be parallel or intersection. Parallel lines never meet. The symbol ‖ is used to indicate “parallel to”. Perpendicular lines form right angles when they intersect. The symbol is used to denote perpendicular lines.

Slide 13 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Vertical and Adjacent Angles When two lines intersect, four angles are formed. Two angles that are opposite each other are called vertical angles. Vertical angles have the same measure. Two angles that share a common side are called adjacent angles. Adjacent angles formed by intersecting lines are supplementary.

Slide 14 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example Find the measure of angles a, b, and c.

Slide 15 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Parallel Lines Parallel Line Cut by a Transversal If two parallel lines are cut by a transversal, then the measure of corresponding angles are equal and the measure of the alternate interior angles are equal.

Slide 16 Copyright © 2015, 2011, 2008 Pearson Education, Inc. Example m || n, find the measures of x, y, and z. y x z 80°