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, read “Point A”A

Points, Lines, and Rays

• If you draw two points on a sheet of paper, a line can be used to connect them

• Lines continue infinitely in both directions while a line segment has 2 endpoints

A B

• AB, “line AB”• AB, “line segment AB”

Points, Lines, and Rays

• A ray is the part of a line that extends without end in one direction

A B C

• In AB, “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 AC)

Points, Lines, and Rays

• A plane is a 2-dimensional surface that extends in all directions

• Named by 3 points on the plane• Plane WSU

S

UW

Importance of Naming

DBN

AE

M

H

I

FL

C

JG

K

P

T

WQ S

V

UR

YX

Z

Points, Lines, and Rays Checkpoint

• Look at the line below:A B C

1. Name a line segment

2. Name a ray in two different ways

3. What is the endpoint of ray BC?Point B

AB, AC, BA, BC, CB, and CA

AB and AC or CB and CA

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 angleA

B C

Naming Angles

• The angle above is made up of BA and BC• Point B is the common endpoint or vertex• Instead of using the word angle, you can

use the symbol for angle, which is

A

B C

Naming Angles

• There are two 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)

• If only given the vertex then use just the letter of the vertex ( B) A

B C

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

2.Name all three of the anglesPoint Y

XYZ, XYW, and WYZ

W

ZYX

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

90º

• A straight angle measures exactly 180º

Classifying Angles

• A reflex angle measures greater than 180º

Classifying Angles• Complementary angles are two angles

whose sum is 90º

• Supplementary angles are two angles whose sum is 180º

Classifying Angles

• You find the complement of an angle by subtracting its measure from 90º

90° - 25°

Classifying Angles

• You find the supplement of an angle by subtracting its measure from 180º

180° - 45°

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. They are formed by the intersection of two lines or line segments.

M NLJJ N M L

Classifying Angles Checkpoint

• Classify each angle below:1) 2)

3) 4)

Obtuse AngleAcute Angle

Straight AngleRight Angle

Classifying Angles Checkpoint

1. What is the relationship between angle a and angle b?

2. What is the relationship between angle a and angle c?

3. Find the measure of angle d if angle a measures 85º.

Vertical Angles, Congruent Angles

Adjacent Angles, Supplementary Angles

Supplementary: 180º – 85º = 95º

Homework

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

Angles (both sides)