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Geometry and Measurement

Chapter 8. Geometry and Measurement. Lines and Angles. 8.1. Planes. A plane is a flat surface that extends indefinitely. Plane. Space extends in all directions indefinitely. Points.

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Geometry and Measurement

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  1. Chapter 8 Geometry and Measurement

  2. Lines and Angles 8.1

  3. Planes A plane is a flat surface that extends indefinitely. Plane Space extends in all directions indefinitely.

  4. Points 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

  5. Lines, Segments, and Rays Line AB or AB Line Segment AB or AB Ray AB or AB A B A B A B

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

  7. Angles An angle can be measured in degrees. There are 360º (degrees) in a full revolution or full circle. 360º

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

  9. Classifying Angles Two angles that have a sum of 90° are calledcomplementary angles. Two angles that have a sum of 180° are calledsupplementary angles.

  10. p q Parallel Lines Two lines in a plane can be either parallel or intersecting.Parallel linesnever meet.Intersecting linesmeet at a point. The symbol  is used to denote “is parallel to.” Parallel lines Intersecting lines p q

  11. m n Perpendicular Lines 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

  12. a d b c Vertical Angles When two lines intersect, four angles are formed. Two of these angles that are opposite each other are calledvertical angles. Vertical angles have the same measure. ma= mc md= mb

  13. a d b c Adjacent Angles Two angles that share a common side are calledadjacent 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

  14. A line that intersects two or more lines at different points is called atransversal. Transversal Lines

  15. Parallel Lines Cut by a Transversal a b d c f e g h If two parallel lines are cut by a transversal, then the measures of corresponding angles are equal andthe measures of thealternate interior angles are equal.

  16. Corresponding angles a b d c f e g h Corresponding angles have equal measures. ma= me mb= mf mc= mg md= mh

  17. Alternate Interior Angles a b c d f e g h Alternate interior angles are angles on opposite sides of the transversal between the two parallel lines. mc= mf md= me

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