Transcript Lesson 1.1 Powerpoint

Lesson 1.1
(And Introduction to Measuring Angles)
Objective:
Recognize points, lines, line segments,
rays, angles, and triangles, and measure
segments, angles, and classify angles
Basic Definitions
Points:
Represented by capital letters
(Draw 3 points and label them)
Lines:
Lines are made up of points and are straight. Arrows
are drawn on the ends to show that the lines extend
infinitely far in both directions.
Basic Definitions
More on Lines:
Lines can be named based on any two points.
Let’s take a look at an example:
Name the line in 3 different ways.
B
A
l
Basic Definitions
Number Line:
A number line is formed when a numerical value is
assigned to each point on a line.
Example:
Draw a number line from -2 to 3 using one tick mark
per integer.
Basic Definitions
Line Segment:
Like lines, segments are made up of points and are
straight, however, segments have a definite
beginning and end.
Line Segments are named by their endpoints.
Examples:
Name the following line segments
S
P
R
X
Q
Basic Definitions
Rays:
Like lines and segments, rays are made up of points
and are straight.
A ray differs from a line or segment in that it begins at
an endpoint and extends infinitely far in only one
direction.
Examples:
M
D
K
C
P
J
L
Note:
It is important to keep in mind that
when we name a ray, we name the
endpoint first! This makes it clear as
to where the ray begins.
Name the following rays:
M
D
K
C
P
J
L
Basic Definitions
Angles:
Two rays that have the same endpoint form an angle.
Def. An Angle is made up of two rays with a
common endpoint. This point is called the vertex of
the angle. The rays are called sides of the angle.
Examples:
P
T
B
2
1
A
C
H
2
S
Naming Angles
When naming an angle with 3 letters you must name
the vertex in the middle! Every time…no exceptions!
Examples:
Name the following angles
P
T
B
2
1
A
C
H
2
S
Triangles
A
A triangle has three
segments as its sides and
three angles at each of its
vertices.
How could you name this
triangle?
B
C
Unions and Intersections
Unions and Intersections are a way to help us see where
certain pieces of an object overlap, and what they form when
A
pieced together.
B
In terms of a triangle:
The triangle is the union (U) of three segments:
ABC  AB  BC  AC
The intersection (∩) of any two sides is a vertex of the
triangle:
AB  BC  B
C
Example #1
A
E
B
a.
AC  DE  ______
b.
AC  BC  ______
c.
BA  BD  ______
D
m
C
Example #2
Draw a diagram in which the intersection of AB with
CA is segment AC
Measuring Segments
Segments can be measured using tools such as
rulers or meter sticks, and often, segments found on
number lines can be measured by subtracting the
ending and starting value.
Example:
P
Q
Measuring Angles
Angles are measured using Protractors, and in this
course we will be measuring angles in degrees.
The measure (or size) of an angle is the amount of
turning you would do if you were at the vertex,
looking along one side, and then turned to look along
the other side. (A surveyor’s transit works in a similar
way!)
Classifying Angles by Size
Angles can be classified into four groups:
Name
Definition
Picture
Acute Angles
Obtuse Angles
Right Angles
Straight
Angles
An angle whose
measure is
greater than 0
and less than 90°
0< x < 90°
An angle whose
measure is
greater than 90°
and less than
180°
90°<x<180°
An angle
whose
measure is 90°
An angle
whose
measure is
180°
Homework
Lesson 1.1 Worksheet