Download 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
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.
Name a line segment
Line segments AB, AC, BA, BC, CB, and CA
2.
Name a ray in two different ways
Ray AB and Ray AC, or Ray CB and Ray CA
3.
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!!!