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# Geometry

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### Geometry

1. 1. GEOMETRY 1
2. 2. Recap Geometrical Terms An exact location on Point a plane is called a point. A straight path on a Line plane, extending in both directions with no endpoints. A part of a line that Line has two endpointssegment and thus has a definite length. A line segment extended Ray indefinitely in one direction
3. 3. POINTS Points are location without substance. They have neither size nor dimension. Points are imperfectly represented on the page by a small dot. A capital letter is used to name a point as we see labeled below. A 3
4. 4. POINTS You have seen points before in the xy- coordinate plane. They are represented by ordered pairs of numbers (x, y). Two intersecting lines intersect in a point. Points make up every geometric figure. For example, string a bunch of them together and you have a line. 4
5. 5. LINES When we talk about lines in geometry we are talking about straight lines that extend forever in both directions. They never end. Below is a picture of a line. When we draw a line we put arrows on the ends to signify that the line keeps going. 5
6. 6. LINES There are two ways to name a line. One way is to use a lowercase letter (usually l, m, n, p, q, r, s, or t) as in the figure below. m 6
7. 7. LINES Two points determine a line, right? Right. What we mean by this is that if you have two different points, there is one and only one line that passes through them. Because of this, another way to name a line is by using two points on the line. Picture of Line Name of Line B     A or AB BA 7
8. 8. LINES So, to name a line by using two points, we write the two capital letters of the points next to each other and then draw a little line symbol over them. It doesn’t matter which letter comes first. Important: the line symbol above the letters has arrows on both ends.   AB 8
9. 9. LINE SEGMENTS Line segments are straight and they have two endpoints. Line segments come in various lengths. Line segments are parts of lines. Below is a picture of a line segment. When we draw one, we usually use dots to emphasize the endpoints. 9
10. 10. LINE SEGMENTS There is only one way we will name line segments. We name them by using their endpoints. A Picture Name or BA B AB 10
11. 11. LINE SEGMENTS When naming a line segment we draw a picture of a line segment (without arrows or dots on the ends) above the two capital letters denoting the endpoints. Note well the difference between the name of a line and the name of a line segment: Line Line Segment   AB AB 11
12. 12. RAYS A ray is straight and it has one endpoint. A ray extends forever in one direction. Imagine a line (not a line segment). If you break the line into two pieces, each piece will be a ray. Below is a picture of a ray. We draw an arrow on one end and a dot on the other end. endpoint 12
13. 13. RAYS We name a ray by using its endpoint and any other point on the ray. We always write the endpoint first, then the other point, and then we draw a picture of a ray above the letters. Picture Name   C D CD 13
14. 14. What Is An Angle ?When two non-collinear rays join with a common endpoint (origin) an angle is formed. Ray BA A Common B endpoint B C Ray BCCommon endpoint is called the vertex of the angle. Ray BA and BC are two non-collinear raysRay BA and ray BC are called the arms of ABC.
15. 15. ANGLES An angle is what you get when you take two rays pointing in different directions and join them at their endpoints. The angle below is formed from the rays     BA and BC. A B C 15
16. 16. Types Of Angles There are four main types of angles.Right Acute angle Obtuse angleangleA A AB C B B C C Straight angle A B C
17. 17. WHAT IS A RIGHT ANGLE?A right angle is an  Right angle angle that measures 90 degrees and forms a square.
18. 18. WHAT IS AN ACUTE ANGLE?  Acute angle An angle that measures less than 90 degrees. “A cute little angle”
19. 19. WHAT IS AN OBTUSE ANGLE?  Obtuse angle An obtuse angle is an angle that measures more than 90 degrees.
20. 20. STRAIGHT ANGLE Straight angle: An angle whose Straight angle measure is 180 degrees A B C A straight angle changes the direction to point the opposite way. It looks like a straight line. 20
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