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Line and Angle Relationships

Line and Angle Relationships. Points , Lines, and Rays. Sometimes it’s necessary to refer to a specific point in space Points have no size The only function of a point is to show position A or Point A. Points, Lines , and Rays.

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Line and Angle Relationships

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  1. Line and Angle Relationships

  2. Points, Lines, and Rays • Sometimes it’s necessary to refer to a specific point in space • Points have no size • The only function of a point is to show position • Aor Point A

  3. Points, Lines, and Rays • If you draw two points on a sheet of paper, a line can be used to connect them • Lines need names just like points do, so we can refer to them easily • Lines continue infinitely in both directions while a line segment has 2 endpoints AB • AB, “line AB” • AB, “line segment AB”

  4. Points, Lines, and Rays • A ray is the part of a line that extends without end in one direction A B C • In AB, “ray AB,” A is the endpoint • The second point that is used to name the ray can be any point other than the endpoint (You could also name it AC)

  5. Points, Lines, and Rays • A plane is a set of line segments or sides that connect to form a closed figure • Plane ABCD or Plane BCDA… A B D C

  6. Points, Lines, and Rays Checkpoint • Look at the line below: A B C • Name a line segment • Name a ray in two different ways • What is the endpoint of ray BC? AB, AC, BA, BC, CB, and CA AB and AC or CB and CA Point B

  7. Naming Angles • Two different rays with the same endpoint form an angle • The point they have in common is called the vertex of the angle • The rays form the sides of the angle

  8. Naming Angles • The angle above is made up of ray BA and ray BC • Point B is the common endpoint or vertex • Instead of using the word angle, you can use the symbol for angle, which is

  9. Naming Angles • There are two ways to name an angle • Using the three letters of the points that make up the two rays with the vertex as the middle letter ( ABC, or CBA) • If only given the vertex then use just the letter of the vertex ( B)

  10. Naming Angles • When more than one angle is formed by a vertex, you use three letters to name each angle • Since A is the vertex of 3 different angles, each angle needs three letters to name it ( CAD, CAB, and BAD)

  11. Naming Angles Checkpoint • Look at the angles formed by the rays below: • Name the vertex • Name all three of the angles Point Y XYZ, XYW, and WYZ

  12. Classifying Angles • An acute angle measures less than 90 degrees • A right angle measures exactly 90 degrees

  13. Classifying Angles • An obtuse angle measures greater than 90º • A straight angle measures exactly 180º

  14. Classifying Angles • A reflex angle measures greater than 180º

  15. Classifying Angles • Complementary angles are two angles whose sum is 90º • Supplementary angles are two angles whose sum is 180º

  16. Classifying Angles • You find the complement of an angle by subtracting it’s measure from 90º

  17. Classifying Angles • You find the supplement of an angle by subtracting it’s measure from 180º

  18. Classifying Angles • Congruent Angles are angles that have the same measure

  19. Classifying Angles • Adjacent angles are two angles that have the same vertex, share a common side, and do not over lap

  20. Classifying Angles • Vertical angles are two opposite and equal angles formed by the intersection of two lines

  21. Classifying Angles Checkpoint • Name each angle below: 1) 2) Obtuse Angle Acute Angle 3) 4) Straight Angle Right Angle or 90 degree Angle

  22. Classifying Angles Checkpoint • What is the relationship between angle a and angle b? • What is the relationship between angle a and angle c? • Find the measure of angle d if angle a measures 85º. Vertical Angles Adjacent Angles, supplementary angles 180º– 85º= 95º

  23. Homework • Skill 1: Lines and Angles (both sides) • Review 64 Points, Lines, Planes, and Angles (both sides) • Due tomorrow!!!

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