Line and Angle Relationships Points Lines and Rays

Line and Angle Relationships

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

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

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)

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

Points, Lines, and Rays Checkpoint • Look at the line below: 1. 2. 3. Name a line segment Line segments AB, AC, BA, BC, CB, and CA Name a ray in two different ways Ray AB and Ray AC, or Ray CB and Ray CA What is the endpoint of ray BC? B

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

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

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)

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)

Naming Angles Checkpoint • Look at the angles formed by the rays below: 1. Name the vertex Y 2. Name all three of the angles Angles XYZ, XYW, and WYZ

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

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

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

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

Classifying Angles • A reflex angle measures greater than 180 degrees

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

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

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

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

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

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

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

Classifying Angles Checkpoint 1. What is the relationship between angle a and angle b? Vertical Angles 2. What is the relationship between angle a and angle c? Adjacent Angles 3. Find the measure of angle d if angle a measures 85 degrees. 180 – 85 = 95 degrees

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