Section 1.1: Getting Started (POINTS, LINES, RAYS, SEGMENTS, ANGLES, ETC.)

Section 1.1: Getting Started(POINTS, LINES, RAYS, SEGMENTS, ANGLES, ETC.) Allie Pusateri, Nicole Madensky, and Brianna Benson

Points • Points represent a location in space. We use capital letters to name them. Points A, B, C, D

Lines Not this kind of line! • Lines are made up of an infinite number of points, are straight, and extend indefinitely far in both directions. -- The line on the left is called line k. -- The line in the middle can be called -- The line on the right can be called line P

Line Segments • Line segments are straight, made up of points, and have a beginning and an end. The segment on the left can be called or The horizontal segment on the right can be called or The other segment that is joined to the horizontal one through A can be called or

Rays • Like lines and line segments, rays are made up of points. • However, a ray begins at an endpoint and then extends indefinitely far in one direction. The ray at the left can be called The ray in the middle can be called The ray at the right can be called

Triangles • A triangle has three segments as its sides. Those segments form three angles. • A triangle is named by its three endpoints. This triangle can be called KDR, KRD, RDK, RKD, DKR, or DRK.

Union and Intersection • A triangle is a union (∪) of three segments. • The intersection (∩) of any two sides of a triangle is a vertex of the triangle. Try using colored pencils to determine the union of segments, lines, or rays. The triangle is the union of three segments. DKR = The intersection of any two sides is a vertex of the triangle = D

Sample Problems K R P F a. How many lines are shown? b. Name these lines. w c. Where do and intersect? d. ∩ = ? e. = ? ANSWERS: a. 2 b. line w, or ; or c. F d. e. D A L a. Name the ray that has endpoint L and goes in the direction of D. b. Name the segment joining A and L. ANSWERS: a or b. or M

Sample Problems Continued Draw a diagram in which = ANSWER: F H G J Draw a diagram in which GHI = L ANSWER:J * K I H *There are other correct answers. L

Explanation for sample problems 1.a. There are two lines because a lines is made of many points and are straight.b. There are many names for these lines because you can name a line by any two points within it.c. They intersect at F because that's where they meet.d. This is where they overlap.e. This is because an angle is made of any two rays that meet at a common vertex. 2.a. There are two different answers to this because there are two points that have an endpoint L and go in the direction of D.b. The segment has two names because you can name a segment in any order. 3.a. To draw this diagram, you must be aware that they must overlap in order to form a segment. 4.a. They intersect at L because this is the point that the triangle and the ray meet.

Practice Problems = ? = ? = ? = ?

Practice Problems Continued = = ? = = ? 4.) 5.) Draw a diagram in which the intersection of and is

Answers to Practice Problems 4.) 3x=15 5.) x=5=AC + 15=BC 15= AB 35= ∆ABC

Works Cited • Milauskas, George, and Robert Whipple. Geometry for Enjoyment & Challenge. Boston: Houghton Mifflin Company, 1991. Print. • "Triangle Cartoons." CartoonStock. Web. 16 Jan. 2010 <http://cartoonstock.com/ directory/T/Triangle.asp>.

Section 1.1: Getting Started (POINTS, LINES, RAYS, SEGMENTS, ANGLES, ETC.)