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)