Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Problem of the Day Draw a clock face that
includes the numerals 112. Draw two lines that
do not intersect and that separate the clock face
into three parts so that the sums of the numbers
on each part are the same.
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Problem of the Day The measure of Jacks angle
is twice that of Amys and half that of Nates.
The sum of the measures of Amys and Trishas
angles is equal to the sum of the measures of
Jacks and Nates angles. The sum of the measures
of all the angles is equal to 180. What is the
measure of each students angle?
Jacks angle 30 Nates angle 60 Amys
angle 15 Trishas angle 75
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Insert Lesson Title Here
MORE WARM-UP
Use the following data set
18, 20, 56, 47, 30, 18, 21. 1. Find the
range. 2. Find the mean. 3. Find the
median. 4. Find the mode.
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30
21
18
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Are you remembering your skills?
WARM-UP
5/6
1) 1 ½ 2 ¾
2) 3 ½ - 2 2/3
4 1/4
9 1/3
1 5/16
3) 3 ½ x 2 2/3
4) 3 ½ ? 2 2/3
5) 2.13 4.5
6) 5.13 - 4.5
6.63
.63
7) 2.13 x 4.5
8) 2.4 ? .02
120
9.585
REVIEW TEST ON THESE THURSDAY
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LETS GO BACK TO 4th grade for a moment
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The building blocks of geometry are points,
lines, and planes.
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Additional Example 1A 1B Identifying Points,
Lines, and Planes Use the diagram to name each
geometric figure.
A. three points
M, N, and P
Five points are labeled points M, N, P, Q, and R.
B. two lines
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Additional Example 1C 1D Identifying Points,
Lines, and Planes Use the diagram to name each
geometric figure.
C. a point shared by two lines
point R
D. a plane
plane QRM
Use any three points in the plane that are not on
the same line. Write the three
points in any order.
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Try This Example 1A 1B Use the diagram to name
each geometric figure.
A. three points
S, T, and U
Five points are labeled points S, T, U, V, and W.
B. two lines
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Try This Example 1C 1D Use the diagram to name
each geometric figure.
C. a point shared by two lines
point W
D. a plane
plane VUT
Use any three points in the plane that are not on
the same line. Write the three
points in any order.
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Additional Example 2A 2B Identifying Line
Segments and Rays Use the diagram to give a
possible name to each figure.
A. three different line segments
B. three ways to name the line
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Additional Example 2C 2D Identifying Line
Segments and Rays Use the diagram to give a
possible name to each figure.
C. six different rays
D. another name for ray AB
A is still the endpoint.
C is another point on the ray.
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Try This Example 2A 2B Use the diagram to give
a possible name to each figure.
A. three different line segments
B. three ways to name the line
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Try This Example 2C 2D Use the diagram to give
a possible name to each figure.
C. six different rays
D. another name for ray DE
D is still the endpoint.
F is another point on the ray.
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CAN YOU ANSWER THESE??? What geometry term might
you associate with each object? 1. a string on
a guitar 2. a window 3. the tip of a pencil 4. a
sheet of paper
line segment
plane or rectangle
point
plane or rectangle
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What did the Acorn say when it grew up?
Gee - I'm -a-tree!
Geometry!
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Angles are everywhere!
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Segersons Warm Up 1. Draw two points. Label
one point A and the other point B. 2. Draw a line
through points A and B. 3. Draw a ray with A as
an endpoint and C as a point on the ray. 4. Name
all the rays in your drawing.
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SOME GEOMETRY JOKES
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Geometry Measurement
Chapter Five
5-1
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TODAY WE WILL...
Learn to name, measure, classify, estimate, and
draw angles.
How do I use this thing?
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Insert Lesson Title Here
Vocabulary
angle vertex acute angle right angle obtuse
angle straight angle
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A Line
A line extends in both directions for evernever
ending!
A
B
AB
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A Ray
A ray has one endpoint and extends without end in
one direction.
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Ray identification
A ray is named by its endpoint and one other
point on the ray. AB
A
B
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An Angle
An angle is two rays with a common endpoint
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Vertex
A vertex is the common endpoint of two rays
Vertex
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Angle Identification
An angle is identified by the three pointsthe
vertex is in the middle!
Written like this!
A
ABC
or
CBA
B
or
B
C
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Angle Measurement
An angle is measured by degrees and can be
classified according to their measures.
Acute Angle Right Angle Obtuse Angle
Straight Angle
less than 90º is 90º more than
90º is exactly 180º
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An angle is formed by two rays with a common
endpoint, called the vertex. An angle can be
named by its vertex or by its vertex and a point
from each ray. The middle point in the name
should always be the vertex. Angles are measured
in degrees. The number of degrees determines the
type of angle. Use the symbol to show degrees
90 means 90 degrees.
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An acute angle measures less than 90.
A right angle measures exactly 90.
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What kind of angle is this?
Right Angle!
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An obtuse angle measures more than 90 and less
than 180.
A straight angle measures exactly 180.
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What kind of angle is this?
Straight Angle!
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Solving Subtraction Equations

• Warm Up
• Simplify.
• x 7 180
• 2. 18 x 90
• 3. 180 x 43
• 4.90 x 47

x 173
x 72
x 137
x 43
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Additional Example 1 Measuring an Angle with a
Protractor Use a protractor to measure the angle.
Tell what type of angle it is.

• Place the center point of the protractor on the
  vertex of the angle.

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Additional Example 1 Continued Use a protractor
to measure the angle. Tell what type of angle it
is.

• Place the protractor so that ray GH passes
  through the 0 mark.

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Additional Example 1 Continued Use a protractor
to measure the angle. Tell what type of angle it
is.

• Using the scale that starts with 0 along ray
  GH, read the measure where ray GF crosses.

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Additional Example 1 Continued Use a protractor
to measure the angle. Tell what type of angle it
is.
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Additional Example 1 Continued Use a protractor
to measure the angle. Tell what type of angle it
is.

• Since 120 gt 90 and 120 lt 180, the angle is
  obtuse.

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What kind of angle is this?
Obtuse Angle!
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Try This Example 1 Use a protractor to measure
the angle. Tell what type of angle it is.
G
I
H

• Place the center point of the protractor on the
  vertex of the angle.

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Try This Example 1 Continued Use a protractor to
measure the angle. Tell what type of angle it is.
G
I
H

• Place the protractor so that ray HI passes
  through the 0 mark.

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Try This Example 1 Continued Use a protractor to
measure the angle. Tell what type of angle it is.
G
I
H

• Using the scale that starts with 0 along ray
  HI, read the measure where ray HI crosses.

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Try This Example 1 Continued Use a protractor to
measure the angle. Tell what type of angle it is.
G
I
H
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Try This Example 1 Continued Use a protractor to
measure the angle. Tell what type of angle it is.
G
I
H

• Since 70 lt 90, the angle is acute.

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What kind of angle is this?
Acute Angle!
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Additional Example 2 Drawing an Angle with a
Protractor Use a protractor to draw an angle that
measures 80.

• Draw a ray on a sheet of paper.

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Additional Example 2 Continued Use a protractor
to draw an angle that measures 80.

• Place the center point of the protractor on the
  endpoint of the ray.

• Place the protractor so that the ray passes
  through the 0 mark.

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Additional Example 2 Continued Use a protractor
to draw an angle that measures 80.

• Make a mark at 80 above the scale on the
  protractor.

• Use a straightedge to draw a ray from the
  endpoint of the first ray through the mark you
  make at 80.

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Try This Example 2 Use a protractor to draw an
angle that measures 45.

• Draw a ray on a sheet of paper.

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Try This Example 2 Continued Use a protractor to
draw an angle that measures 45.

• Place the center point of the protractor on the
  endpoint of the ray.

• Place the protractor so that the ray passes
  through the 0 mark.

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Try This Example 2 Continued Use a protractor to
draw an angle that measures 45.

• Make a mark at 45 above the scale on the
  protractor.

• Use a straightedge to draw a ray from the
  endpoint of the first ray through the mark you
  make at 45.

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To estimate the measure of an angle, compare it
with an angle whose measure you already know. A
right angle has half the measure of a straight
angle. A 45 angle has half the measure of a
right angle.
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Now, lets go to 6th grade!
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WARM UP

• Draw a 45 degree angle without a protractor
• Draw a 135 degree angle without a protractor
• Draw a 10 degree angle without a protractor
• THEN, check to see if you were correct by using a
  protractor

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Additional Example 3 Estimating Angle
Measures Estimate the measure of the angle, and
then use a protractor to check the reasonableness
of your estimate.
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Lets take a commercial break
Adult
Child
Can think about what they cant see
Can think about what they can see
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That is what this was all about!
Can you see it?
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That is what this was all about!
Can you see it?
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Can you see it?
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Can you see it?
At first glance, tell me what you see! Do you see
a vase? Or do you see something more. Look
Closely!!!!
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Additional Example 3 Estimating Angle
Measures Estimate the measure of the angle, and
then use a protractor to check the reasonableness
of your estimate.
Can you see it?
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Additional Example 3 Estimating Angle
Measures Estimate the measure of the angle, and
then use a protractor to check the reasonableness
of your estimate.
Can you see it?
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Additional Example 3 Estimating Angle
Measures Estimate the measure of the angle, and
then use a protractor to check the reasonableness
of your estimate.
Can you see it?
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Additional Example 3 Estimating Angle
Measures Estimate the measure of the angle, and
then use a protractor to check the reasonableness
of your estimate.
About half of 90
Can you see it?
90
90 plus 45 135
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Can you see it?
So.. Estimate the measure of the angle, and then
use a protractor to check the reasonableness of
your estimate.
Think The measure of the angle is about halfway
between 90 and 180. A good estimate would be
135.
The angle measures 131, so the estimate is
reasonable.
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CAN YOU SEE THIS ONE? Estimate the measure of the
angle, and then use a protractor to check the
reasonableness of your estimate.
Think The measure of the angle is a little more
than halfway between 0 and 90. A good estimate
would be 50.
The angle measures 52, so the estimate is
reasonable.
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How about this one
Can you see it?
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About 20-25
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How about this one
Can you see it?
About 165-170 or so
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How about this one
Can you see it?
85 or so?
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Insert Lesson Title Here
Warm-up
Use a protractor to draw an angle with the given
measure. Tell what type of angle it is. 1. 130
2. 26 3. Draw a right angle. 4. Is the angle
shown closer to 30 or 120?
obtuse
acute
30
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How do I use a protractor?
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Protractor
A protractor is used to measure angles in
degreesº
140º
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Protractor
Place the Vertex of the angle in the middle.
220º
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Protractor
How do you know which number to use220º or 40º?
An obtuse angle!
220º
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Protractor
A right angle!
90º
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Protractor
An Acute angle!
45º
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Congruent
If two angles have the same measure, they are
congruent
Ã
Ã
40º
40º
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Congruent means The same measure
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Find Congruent Angles!