Transcript Line and Angle Relationships

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”
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
Importance of Naming
Points, Lines, and Rays
Checkpoint
• Look at the line below:
A
1.
B
C
Name a line segment
AB, AC, BA, BC, CB, and CA
2.
3.
Name a ray in two different ways
AB and AC or CB and CA
What is the endpoint of ray BC?
Point 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
A
B
C
Naming Angles
A
B
C
• 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
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
A
letter of the vertex ( B)
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
W
below:
X
Y
1.Name the vertex
Point Y
2.Name all three of the angles
XYZ,
XYW, and
WYZ
Z
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.
J
N
J
M
N
L
M
L
Classifying Angles Checkpoint
• Classify each angle below:
1)
2)
Obtuse Angle
3)
Acute Angle
4)
Straight Angle
Right Angle
Classifying Angles Checkpoint
1. What is the relationship between angle a
and angle b? Vertical Angles, Congruent Angles
2. What is the relationship between angle a
and angle c? Adjacent Angles, Supplementary Angles
3. Find the measure of angle d if angle a
measures 85º. Supplementary: 180º – 85º = 95º
Homework
• Skill 1: Lines and Angles (both sides)
• Review 64 Points, Lines, Planes, and
Angles (both sides)