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Chapter 1: Tools of Geometry

Chapter 1: Tools of Geometry. Objectives: To understand basic terms of Geometry To apply the segment and angle addition postulates. Vocabulary. Line: A series of points that extends in 2 opposite directions without end

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Chapter 1: Tools of Geometry

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  1. Chapter 1: Tools of Geometry Objectives: To understand basic terms of Geometry To apply the segment and angle addition postulates

  2. Vocabulary Line: • A series of points that extends in 2 opposite directions without end • Can name a line by any two points on the line with a line above it, or by a single lower case letter. (Please note: In Geometry, it is important to use the correct notations!!)

  3. Collinear Points • Points that lie on the same line.

  4. Use the following image to answer the questions. • Name a line. • Are points A, B, and E collinear? • Name 3 collinear points.

  5. PLANES • A flat surface that has no thickness • Contains many lines • Extends w/o end in the direction of all its lines • Named by a single capital letter OR by AT LEAST 3 NONCOLLINEAR POINTS Coplanar: Points and lines on the same plane.

  6. Are P, B and A collinear? Explain.

  7. Vocabulary • Segment: part of the line consisting of 2 endpoints and all the points between them • How you name a segment: • Ray: part of a line consisting of one endpoint and all the points of the line on one side of the endpoint • How you name a ray:

  8. Opposite Rays Two collinear rays with the same endpoint. Opposite rays form a line. • and are opposite rays. • Are and opposite rays? Why or why not? R Q S

  9. Be careful…. When naming a segment: When naming a ray: Must name the endpoint first then any other point on the ray in the direction of the ray ORDER MATTERS!! • Use both endpoints to name • Order in which you name the endpoints does NOT matter

  10. Parallel Lines Parallel Lines: COPLANAR lines that do not intersect (to name parallel lines, you can use the symbol ||)

  11. 1. Name 2 parallel segments.

  12. Parallel Planes F Planes that do not intersect Example: 1. Name a plane parallel to plane EDA. E C D H G B A

  13. 2 segments with the same length are:CONGRUENT SEGMENTS ( ) C A A B 2 cm 2 cm AB = CD DON’T SAY Equal signs only compare numbers, never geometric figures

  14. Find the length of each segment. A B C D E AB= BC= BE= WHICH TWO SEGMENTS ARE ?

  15. Segment Addition Postulate AB + BC = AC If AB = 5, and BC = 2, then AC = (The sum of the parts equals the whole) A C B

  16. Given: . B is between A and C 1.If AB = 20 and AC = 35, what is the length of BC? 2. AC = 100 AB= 4x -20 BC = 2x +30 Find x, AB, and BC.

  17. Naming an Angle ANGLE ( ): Formed by 2 rays with the same endpoint To name an angle: To indicate angle measure:

  18. Angles with a shared vertex: Must name using a numbered angle or using 3 points with vertex in the middle.

  19. Angle Addition Postulate B A C O If the m AOC= 98°, and m AOB=65°, find the m BOC.

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