Everyday Math Everyday Math 3.33.3Exploring Angle Measures

Math MessageMath MessageHow 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?

Math Message Follow-UpMath Message Follow-UpDraw 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?

Symbol of an angle is…Symbol of an angle is…

Sometimes an angle is named with a single capital letter ( B)

This point is called Vertex.

Vertex is where the 2 lines come together.

B

Ways to name anglesWays to name angles..(copy ..(copy

symbol in composition book)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.

A

R

M

This angle can be named as A or RAM

Degrees in a circle =Degrees in a circle =0

90

Angles..Angles..Acute- between 1 and 89 degrees

Obtuse- between 91 and 179 degress

Right- has 90 degrees

AN

G

J

A

B

Everyday Math 3.4Everyday Math 3.4Using 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.

New Angles….New Angles….

Straight Angles = 180

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

ProtractorProtractor

The key to using a half-circle The key to using a half-circle projector is….projector is….Knowing which scale to read…..

Estimate..Estimate..You should always estimate

whether the angle is more or less than 90 .

Examples….A

B

C

Lines.. Look around the room Lines.. Look around the room for…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.

Work on Math Journal pg. Work on Math Journal pg. 7070

Reflex

And always look to see if you are measuring the in or outside of the angle.

Then page 71, #4-5

Move on to page 71Move on to page 71Only do numbers 4 & 5.

Math 3.5Math 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.

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.

Measuring Angles Formed by Measuring Angles Formed by Intersecting LinesIntersecting LinesWhat are Vertical or Opposite

angles?

40° 40°

A D

B E

C

Use these angles to try and define what vertical or opposite angles are.

Adjacent AnglesAdjacent Angles

G

HIF

130° 50°

Use this angle to define Adjacent Angles.

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

What do we use to draw What do we use to draw circles?circles?A compass..

How do we use it to make a large circle?

How do we use it to make a small circle?

3.6 Identifying Triangles3.6 Identifying TrianglesEquilateral 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.

Label the Triangles…Label the Triangles…

What are these marks?

The Marks….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..

Congruent Triangles Congruent Triangles are…..are…..

The same size and the same shape…

Open up Math Journal pg. Open up Math Journal pg. 7777Complete notes part IV A-E

Homework-SL 3.6

Two ways to classify or to Two ways to classify or to name Trianglesname Triangles

By angles

Acute ObtuseRight

By lengths of their sides..

IsoscelesEquilatera

lScalene

The MAGIC Number for The MAGIC Number for Triangles is 180……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

45 tFind the missing

angle.

45

26

77

t

t

3.73.7

Properties of Properties of PolygonsPolygons

Cut out Shapes from Activity Cut out Shapes from Activity 4 in the back of your 4 in the back of your Journals.Journals.

What are these shapes?

Polygons are closed figures with straight edges. (no rounded sides or open

figures)

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?

Turn to page 78Turn to page 78

3.8 Tessellations3.8 Tessellations

What is a Tessellation?

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

Discuss the characteristics you observe.

Characteristics of Characteristics of TessellationsTessellationsSome 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.

Take a guess..Take a guess..What is the definition for a

“regular polygon.”

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

A tessellation consisting of regular polygons is

called a “regular tessellation.”

Let’s Practice…Let’s Practice…Open up page 86 and 87 in your

Math Journal.

3.9 Angles of Polygons3.9 Angles of PolygonsLets review

Pentagon has ___sidesHexagon has ___sidesHeptagon has ___sidesOctagon has ___sidesNonagon has ___sidesDecagon has ___sides

Math Journal page 88 # Math Journal page 88 # 1,2,3,41,2,3,4Math Journal page 89 #7Math Journal page 90 # 9,10Math Journal page 91 # 1,2Math Journal page 92 # 1-5

HW math boxes 3.7 # of sides minus 2 X 180 =___°

Polygon Worksheet ( Click) ( Click)

3.10 Solving Problems Using 3.10 Solving Problems Using the Geometry Templatethe Geometry Template

Draw a circle with your Draw a circle with your template and two pencils…template and two pencils…

Now open up Math Now open up Math Journal to page 96… Journal to page 96… only do the EVEN only do the EVEN problems.problems.