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Line and Angle Relationships

Learn about points, lines, and angles in geometry, including how to name and measure angles. Understand the relationships between different elements in space. Practice identifying and classifying angles for better geometry comprehension.

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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 • .A or 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 • Line segment AB or • Line AB or AB

  4. Points, Lines, and Rays • Since the length of any line is infinite, we sometimes use parts of a line • A ray is the part of a line that extends without end in one direction • In “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 ray 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 A B D C

  6. Points, Lines, and Rays Checkpoint • Look at the line below: • Name a line segment • Name a ray in two different ways • What is the endpoint of ray BC? Line segments AB, AC, BA, BC, CB, and CA Ray AB and Ray AC, or Ray CB and Ray CA 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 • B is the common endpoint • Point B is the vertex of the angle • Instead of using the word angle, you can use the symbol for angle, which is

  9. Naming Angles • There are several 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) • 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 Y Angles XYZ, XYW, and WYZ

  12. Measuring Angles • You measure an angle in degrees using a protractor • Place the center point of the protractor on the vertex of the angle • Align the 0 degrees line on the protractor with one side of the angle • Read the number of degrees on the scale where it intersects the second side of the angle

  13. Measuring Angles Checkpoint • Measure each angle Answers should be close to 60, 30, and 20 degrees. On my projector, the line covers about 10 degrees

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

  15. Classifying Angles • An obtuse angle measures greater than 90 degrees • A straight angle measures exactly 180 degrees

  16. Classifying Angles • A reflex angle measures greater than 180 degrees

  17. Classifying Angles • Complementary angles are two angles whose sum is 90 degrees • Supplementary angles are two angles whose sum is 180 degree

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

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

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

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

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

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

  24. 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 85 degrees. Vertical Angles Adjacent Angles 180 – 85 =95 degrees

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

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