Geometry and Measurement Chapter Nine

Lines and Angles Section 9.1

Plane A plane is a flat surface that extends indefinitely. Space extends in all directions indefinitely. 3 Martin-Gay, Prealgebra, 5ed

Point The most basic concept of geometry is the idea of a point in space. A point has no length, no width, and no height, but it does have location. We will represent a point by a dot, and we will label points with letters. A Point A 4 Martin-Gay, Prealgebra, 5ed

AB A B Line AB or AB Ray AB or AB Line Segment AB or AB AB 5 Martin-Gay, Prealgebra, 5ed

Vertex An angle is made up of two rays that share the same endpoint called a vertex. The angle can be named,,, or. The angle can be named  ABC,  CBA,  B, or  x. A B C x The vertex is the middle point. 6

An angle can be measured in degrees. There are 360º (degrees) in a full revolution or full circle. 360º 7 Martin-Gay, Prealgebra, 5ed

Classifying Angles Acute Angle Name Angle Measure Examples Between 0° and 90° Right Angle Exactly 90° Obtuse Angle Between 90° and 180° Straight Angle Exactly 180º 8

Two angles that have a sum of 90° are called complementary angles. Two angles that have a sum of 180° are called supplementary angles. 9 Martin-Gay, Prealgebra, 5ed

Two lines in a plane can be either parallel or intersecting. Parallel lines never meet. Intersecting lines meet at a point. The symbol  is used to denote “is parallel to.” p q Parallel linesIntersecting lines p  q 10 Martin-Gay, Prealgebra, 5ed

Two lines are perpendicular if they form right angles when they intersect. The symbol  is used to denote “is perpendicular to.” Perpendicular lines n m n  mn  m 11 Martin-Gay, Prealgebra, 5ed

When two lines intersect, four angles are formed. Two of these angles that are opposite each other are called vertical angles. Vertical angles have the same measure. a b c d a  cd  b 12 Martin-Gay, Prealgebra, 5ed

Two angles that share a common side are called adjacent angles. Adjacent angles formed by intersecting lines are supplementary. That is, they have a sum of 180 °.  a and  b  b and  c  c and  d  d and  a a b c d 13 Martin-Gay, Prealgebra, 5ed

A line that intersects two or more lines at different points is called a transversal. 14 Martin-Gay, Prealgebra, 5ed

Parallel Lines Cut by a Transversal If two parallel lines are cut by a transversal, then the measures of corresponding angles are equal and alternate interior angles are equal. 15 Martin-Gay, Prealgebra, 5ed

Corresponding angles are equal. a b c d e f gh 16 Martin-Gay, Prealgebra, 5ed

Alternate interior angles are angles on opposite sides of the transversal between the two parallel lines. a b c d e f gh 17 Martin-Gay, Prealgebra, 5ed