Everyday Math 3.3

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Everyday Math 3.3

• Exploring Angle Measures

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Math Message

• How might you prove that the measure of each
  angle of a square is 90 degrees? Be prepared to
  explain your answer. (Hint What is the total
  number of degrees in a circle?

3
Math Message Follow-Up

• Draw one large square and divide it into 4
  squares.
• Draw a circle. What is the total number of
  degrees in the circle?
• Draw the circle into four equal parts.
• What kind of angle does that create?
• How many degrees does that angle have?

4
Symbol of an angle is
This point is called Vertex.
B
Sometimes an angle is named with a single capital
letter ( B)
Vertex is where the 2 lines come together.
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Ways to name angles..(copy symbol in composition
book)

• Not only is the angle named with a single letter,
  sometimes an angle is named with 3 letters The
  middle letter names the vertex and the other two
  letters name points, one on each side of angle.

R
A
M
This angle can be named as A or RAM
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Degrees in a circle
0
90
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Angles..

• Acute- between 1 and 89 degrees
• Obtuse- between 91 and 179 degress
• Right- has 90 degrees

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A
N
G
A
J
B
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Everyday Math 3.4

• Using a Protractor
• Review- Acute angle is greater than 0 degrees and
  less than 90 degrees.
• Obtuse is an angle whose measure is greater than
  90 degrees and less than 180 degrees.
• Right angle is 90 degrees.

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New Angles.

• Straight Angles 180
• Reflex angle is greater than 180 and less then
  360. (Students bend your arms to show a straight
  angle)

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Protractor
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The key to using a half-circle projector is.

• Knowing which scale to read..

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Estimate..

• You should always estimate whether the angle is
  more or less than 90 .
• Examples.

A
B
C
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Lines.. Look around the room for

• Perpendicular lines or line segments intersect to
  form a right or 90 degree angle.
• Parallel lines remain the same distance apart
  over their entire length. No matter how far you
  extend them, they will never meet.
• An intersection is a single point where two lines
  meet or cross each other.

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Work on Math Journal pg. 70
And always look to see if you are measuring the
in or outside of the angle.
Reflex
Then page 71, 4-5
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Move on to page 71

• Only do numbers 4 5.

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Math 3.5

• Parts of a Circle
• Can you tell me where the radius is on a circle?
• How about the diameter of a circle?
• What if I told you that the diameter equals the
  radius multiplied by two.

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Radius is any line segment from the center of the
circle to any point on the circle.
Diameter is any line segment that passes through
the center of the circle and has endpoints on the
circle.
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Measuring Angles Formed by Intersecting Lines

• What are Vertical or Opposite angles?

A
D
Use these angles to try and define what vertical
or opposite angles are.
40
40
C
B
E
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Adjacent Angles
G
130
50
H
I
F
Use this angle to define Adjacent Angles.
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• Vertical or Opposite Angles are when two lines
  intersect, the measures of the angles opposite
  each other are equal.
• Adjacent Angles are angles that are next to each
  other and have a common side.
• Use these definitions to complete Math Journal
  page 75

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What do we use to draw circles?

• A compass..
• How do we use it to make a large circle?
• How do we use it to make a small circle?

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3.6 Identifying Triangles

• Equilateral triangle has three sides that are the
  same length.
• Isosceles triangle has at least two sides that
  are the same length.
• Scalene triangle has no sides of the same length.

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Label the Triangles
What are these marks?
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The Marks.

• Can simply be called marks. Other names are hatch
  marks, slash marks, and tick marks.
• What are their purpose?
• The marks indicate sides of the same length in
  the given figure.

For example..
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Congruent Triangles are..

• The same size and the same shape

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Open up Math Journal pg. 77

• Complete notes part IV A-E
• Homework-SL 3.6

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Two ways to classify or to name Triangles

• By angles
• Acute
• Obtuse
• Right

• By lengths of their sides..
• Isosceles
• Equilateral
• Scalene

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The MAGIC Number for Triangles is 180

• When we try to find the missing angles of a
  triangle, it is very important to remember we
  want numbers that add up to 180.

85
Find the missing angle.
t
45
30
45
26
t
77
t
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3.7 Properties of Polygons
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Cut out Shapes from Activity 4 in the back of
your Journals.

• What are these shapes?
• Polygons are closed figures with straight edges.
  (no rounded sides or open figures)

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• Sort the 16 polygons into 2 or 3 different sets
  according to any rule that you make up.
  (examples-at least one pair of parallel sides
  versus no sides parallel. Or at least one angle
  greater than 90 degrees versus all angles acute
  or right.)
• What are some of the rules you came up with?

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Turn to page 78
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3.8 Tessellations

• What is a Tessellation?

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• Tessellation is an arrangement of repeated closed
  shapes that cover a surface so that no shapes
  overlap, and there are no gaps between shapes.

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Discuss the characteristics you observe.
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Characteristics of Tessellations

• Some tessellations repeat only one basic shape.
  Others combine 2 or more basic shapes.
• In a tessellation, the basic shapes are
  translated (slid), rotated (turned), or reflected
  (flipped) to fill the surface.

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Take a guess..

• What is the definition for a
• regular polygon.

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• Regular polygons- all of the sides are the same
  length and all of the angles have the same
  measure.

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• A tessellation consisting of regular polygons is
  called a regular tessellation.

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Lets Practice

• Open up page 86 and 87 in your Math Journal.

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3.9 Angles of Polygons

• Lets review
• Pentagon has ___sides
• Hexagon has ___sides
• Heptagon has ___sides
• Octagon has ___sides
• Nonagon has ___sides
• Decagon has ___sides

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Math Journal page 88 1,2,3,4

• Math Journal page 89 7
• Math Journal page 90 9,10
• Math Journal page 91 1,2
• Math Journal page 92 1-5
• HW math boxes 3.7

of sides minus 2 X 180 ___
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Polygon Worksheet ( Click)
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3.10 Solving Problems Using the Geometry Template
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Draw a circle with your template and two pencils
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Now open up Math Journal to page 96 only do the
EVEN problems.