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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
WHAT IS A RIGHT ANGLE?A right angle is an Right angle angle that measures 90 degrees and forms a square.
WHAT IS AN ACUTE ANGLE? Acute angle An angle that measures less than 90 degrees. “A cute little angle”
WHAT IS AN OBTUSE ANGLE? Obtuse angle An obtuse angle is an angle that measures more than 90 degrees.
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