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Section 1.1

Section 1.1. By Mia Gurganus and Lauren Archibald. Points. A point is a dot named with a capital letter. Ex. M A Z

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Section 1.1

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  1. Section 1.1 By Mia Gurganus and Lauren Archibald

  2. Points • A point is a dot named with a capital letter. • Ex. M A Z K

  3. Lines • A line is made up of points that are straight. • Lines are named after any two points on it. (Hint: Lines have arrows on the ends of them to indicate that they go on forever in both directions) • Ex. 2. M N 1. AB 3. GJ Line 1: AB Line 2: NM Line 3: GJ

  4. Line Segments and Rays • Line segments are made up of points, are straight, and have a definite beginning and end. B • Rays are made up of points and are straight. A ray begins at an endpoint and extends infinitely far in only one direction. Rays must be named with the endpoint first so it is clear where the ray begins. A B This ray can only be represented as AB The segment could be represented as AB or BA A

  5. Number Lines • A number line forms after a numerical value is assigned to each point on the line. • Ex. F P -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 The coordinate of F is 0. The coordinate of P is 3.

  6. Angles • An angle is the union of two rays with a common endpoint. • The point where the two rays meet is called the vertex of the angle. • The rays are called sides of the angle. • When naming an angle, three letters are used. The vertex letter must be named in the middle. You could also simply name the angle by the vertex point’s letter. G M H This angle could be named: <GMH, <HMG, or <M.

  7. Triangles • A triangle is a figure with three segments as its sides. Not only does it have three sides, but it has three angles as well. K The figure would be called triangle KLM ( KLM). <K, <L, and <M are all angles within the triangle L M

  8. Union and Intersection K KL, LM, and KM all join KML, so you would say that KML = KL LM KM. • A triangle is the union of three segments. ( ) • The intersection of any two sides is a vertex of the triangle. ( ) KL LM = L LM KM= MFor example, in the triangle above, KM KL = K KL and LM meet at point L. The point of intersection is L. M L

  9. Practice Problems True or False • 1. A point is named with a capital letter. • 2. Lines go on forever in one direction. • 3. An angle is made up of two segments with a common endpoint. • 4. When naming an angle with more than one letter, the vertex letter must be in the middle. • 5. A segment is named after its two endpoints. • 6. When naming a ray, name the endpoint second. • 7. A triangle is the intersection of three points. • 8. The intersection of any two sides is a vertex of the triangle.

  10. More Practice Problems 1. Name the coordinate of K. 2. Name all possibilities for the angle. K L Z 1 2 3 4 5 6 7 R 3. Name where OP intersects PT in OPT. 4. Name the ray. O Y W P T

  11. Answers Practice ProblemsMore Practice Problems • 1. True 1. The coordinate of K is 4. • 2. False 2. <LZR, <Z, or <RZL. • 3. False 3. P • 4. True 4. YW • 5. True • 6. False • 7. False • 8. True

  12. Works Cited Rhoad, Richard, George Miluaskas, and Robert Whipple. Geometry for Enjoyment and Challenge. New Edition ed. Boston: McDougal Littell, 1997. Print.

  13. The End

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