miin Web viewCB = BA. Circle the capital ... Palliser’s Triangle has a base of approximately...

Unit 8 Math Name: _________________

Mrs. Clement Teacher Check________________

Unit 8: Geometry, Measurement & Circles

+ I understand what this is and can do it very well√ I understand and can do most of this

;) I Get this − I have some trouble with thisPre-quiz

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Lesson Key WordsPractice

Questions/ Projects

Jump Math Extras

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What You’ll Learn...• To draw line segments parallel to another line segment• To draw a line segment perpendicular to another line

segment• To daw a line that divides a line segment in half and is

perpendicular to it• To divide an angle in half• To develop and use formulas to calculate the areas of

triangles and parallelograms• To construct and draw a circle• To estimate and calculate circumference• To estimate and calculate area and circumference of circles

Why is it important?

• Airports, building developments, shopping malls, schools, houses and parks all require knowledge of angles, area, bisecting lines and circles.

• Streets are built using grids, airports have bisecting line segments and soccer fields have parallel lines.

• Circles are all around us. The sun, the earth, the planets; if you draw across section of a tree, plant stem or flower; DVD’s, coin, wheel and Smarties. A drum, a tepee, a medicine wheel, a medallion, a talking circle…Why is this shape SO important to cultures around the world? Why does it have sacred and mystical meaning?

Unit 8 MathMrs. Clement

8.1 Parallel and Perpendicular Line Segments

Draw a line segment with parallel lines

Draw a line segment with right angles

ParallelPerpendicular

HW: 12-13 97-99100-101109-11

8.2 Draw perpendicular Bisectors

Draw a line that divides a line segment

Perpendicular bisector

HW: 17 105-106107-108

8.3 Draw Angle Bisectors Draw lines that divide

angles in half

Angle bisector

HW: 21 102-104117

8.4 Area of a Parallelogram Develop area formulas Calculate area of

parallelogram

ParallelogramBaseheight

HW: 24-25

HW:33

170-171118-119

8.5 Area of a Triangle Develop formula for

triangles Calculate area of triangle

HW:38-39 172-175112-116

8.6 Construct Circle Draw circles with given

radius or diameter Determine diameter Determine radius

RadiusDiameter

INQUIRYPROJECT

(7.2 115)197-98

8.7 Circumference of a Circle Estimate and calculate

circumference Solve equations

Circumference

HW:44 199-200

8.9 Area of a Circle How to determine area Estimate and calculate area Solve equations

PiCircle graphSectorCentral angle

HW: 49-50 201-204

Unit 8 Quiz

× I have a big problem with this

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8.1 Parallel and Perpendicular Line SegmentsHow can we draw a line segment with parallel lines/ angles? (textbook. 82-88)

You are about to build a greenhouse and decide to Google images for inspiration. You see several designs that you like:

Which one do you choose?

Why did you choose this design?

Which design provides the most stability? How do you know?

Which design is the easiest to construct, do you think? How do you know?

Which design is the most labour-intensive? How do you know?

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Points and LinesMatch the following term to the correct diagram

ExploreExample #1: Draw a point on each line and choose a letter to name it.

Example #2: Draw two points on each line. Name the lines.

line __________ line __________

Example #3: Draw and name any line

Try it Out:

Point

Line(no endpoint)

line segment(2 endpoints)

ray(1 endpoint)

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1. Draw a line segment PQ of a length of 5cm

2. Circle the endpoint of each ray and name points.

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ray: ______

ray: ______

3. Name each ray.

ray: _______ and _______ ray ______ and _________

4. Give an example of intersecting lines in your classroom: _________________________________

5. Name the intersecting lines and the intersecting point.

You don’t need to draw arrows and/or dots at the end of lines, rays and line segments unless you especially want to show that what you are drawing is a line, ray, or line segments.

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_____ and _____ intersect at ______ ____ and ____ intersect at _______

6. Circle the intersecting point.

7. Label the lines. Find two of each object in this image:a. Point: _____ and _____b. Line: _____ and _____c. Line segment: _____ and

_____d. Ray: _____ and _____

Bonus: Two intersecting edges of the prism are marked. Trace another pair of intersecting lines.

Identifying Parallel and Perpendicular Line Segments

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Are there line segments in this image? Are the lines parallel? Are the lines perpendicular?

Label two horizontal line segments: AC, DF and one vertical line segment BE. Measure the lines between AC and DF in two locations. If the measurements are the same, the lines are parallel.

Place a protractor at point E on line segment DF. If angle BEF or BED measures 90 degrees, the lines are perpendicular.

Name each part of the geometry kit:

Set square

Protractor

Ruler

Compass

Pencil, eraser, sharpener

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Draw Parallel line segments:

Draw Perpendicular line segments:

Draw a line segment, AB. Draw another line segment, CD, parallel to AB.

Slide the triangle along the ruler. Draw along the perpendicular edge of the triangle to create a line parallel to AB. Label the endpoints of the parallel line segment C and D.

Use a ruler to draw the line segment. Label its endpoints A and B. Place the edge of a right angle along AB as shown. Place a ruler against the bottom edge of the triangle.

Draw a line segment, EF. Draw another line segment, GH perpendicular to EF.

Use a ruler to draw the line segment. Label its endpoints E and F. Mark a point along the line and label G.

Place a protractor at point G. Mark the point that is at right angles with line segments EF. Label it H.

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Parallel Lines

ExploreExample #1: Extend both lines. Use a ruler. Do the lines intersect or are they parallel?

Example #2: Match the descriptions to the lines.

A. The lines intersectB. If the lines were extended far enough, they lines would intersectC. The lines are parallel

_________ __________________

Example #3: Give two examples of parallel lines you see around you: ________________________ ________________________

Parallel lines never intersect, no matter how far they are extended in either direction.

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Try it Out:

1. Use arrow symbols to mark the sides or edges of the shapes that look like they are parallel.

2. Name each line. State which lines are parallel.

_____ ll _____ _____ ll _____ _____ ll _____

Try it Out:

We mark parallel lines using an equal number of rows symbol. The ll means “it is parallel to.”

Determining if two lines are parallelIf two lines are perpendicular to one another, then they are parallel.

If two lines are parallel, any line perpendicular to one of the parallel lines will be perpendicular to the other.

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1. Mark any parallel lines. State which lines are parallel.

EF ll _______ _______ll _______ _______ll _______

2. Circle the flags that contain parallel lines (not including the edge of the flag)

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Homework Due Date: _________________

Perpendicular Lines

1. Name the

perpendicular lines.

Perpendicular lines meet at a right angle (90°). The symbol means “is perpendicular to.”

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AB _____ _____ _____ _____ _____

2. Are the pairs of lines below perpendicular or parallel? Measure the angle where they meet to check. Draw a square corner ⊾ to show any perpendicular angles.

3. Look at these examples of perpendicular lines in real life. Draw the perpendicular lines and label.

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4. Use a set square. Draw a line segment perpendicular to AD that passes through C. Label the line. Draw a line that is parallel to the new line that passes through B.

5. A rectangle has 4 right angles. Draw the missing sides to complete rectangle ABCD.

Homework Reflection:

Which parts of the homework did you find pretty straightforward?

Which parts challenged you?

If you had difficulty with a certain question, what strategies did you use to solve the problem?

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8.2 Draw Perpendicular BisectorsHow can we draw a line that divides a line segment? (textbook. 89-94)Explore

Example #1: Fill in the blanks to find the midpoint of this line segment

.

Length of the line segment = ______ cm

Length ÷ 2 = ____ cm

Mark the midpoint on the line.

Example #2: Determine the midpoint of each line segment. Use a ruler.

Try it Out:

This scale is missing its perpendicular bisector support. How can you figure out where the support should be?

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1. Use a set square or protractor to draw the perpendicular bisector of each line segment. The midpoint is marked.

2. Draw the perpendicular bisector of each line segment.

3. Bisector Murder Mystery: Look at the following clues. Do you think you can recreate the “bisector crime scene” based on the evidence provided?

a. D is the midpoint of FGb. BH is perpendicular to AC and GFc. The intersection of point CE is FG is Dd. FG is the perpendicular bisector of BHe. CE is a bisector of BHf. CB = BA

4. Circle the capital letters in the set below that contain perpendicular bisectors.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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How to Draw a Perpendicular Bisector

A. Use a compass

Step 1: choose a point at each end of the soccer field. Label one point A and the other B.

Step 2: Open the compass and draw a circle, keeping the compass point on point A. Draw another circle on point B.

Step 3: Use a ruler to draw a line segment from C to D. CD is the perpendicular bisector of AB.

B. Use a right triangle

Step 1: choose a point at each end of the field. Label them A and B.

Step 2: Measure from point A to point B. Mark the midway point.

Step 3: Use a right triangle to draw a line segment at point C perpendicular to AB.

A soccer field needs to be repainted with straight lines. Unfortunately, all you have is a rope. Suddenly you have an ingenious idea. You will use the rope to make perfectly straight lines. How do you do it?

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Build a Soccer Field using Bisecting Angles

Your assignment for this unit will be to build a soccer field using only a compass and a ruler. Create a rough idea of how you might do this. You must show evidence of using bisecting lines and angles. In other words, DO NOT ERASE YOUR LINES.

NOT SO GOOD GOODGREAT

Video Tutorial: “Bisecting a line: a geometric construction” (2:48) SocratiaStudies

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8.3 Draw Angle Bisector

How can we draw lines that divide angles in half? (textbook. 95-100)

Circles and Shapes

Use a compass:

Step 1: Draw and label the angle DEF. Place your compass point on E. Draw an arc from D to F.

Step 2: Place your compass on points on A and draw an arc. Then place the compass on C and draw an arc. Label the point of intersection I.

Step 3: Use a ruler to connect B to I.

Use a protractor:

Step 1: Draw and label the angle DEF. Measure the angle. Divide the angle in half. Example: 110 ÷ 2 = 55.Label this point I.

Step 2: Use a protractor to check your angle.

Step 3: Use a ruler to connect E to I

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Explore

Example #1: Circle the vertex on each angle.

Example #2: Fill in the blank to name each angle in two ways.

∠PQ ___ or

∠ ___QP

∠ __B __ or ∠ __ B __ ∠ __T __ or ∠ __ T __

Example #3: Circle the vertex, then name the angle.

∠ ___ G ___ ∠ ___ ___ ___ ∠ ___ ___ ___

BONUS: circle all the possible names for the angle

Measuring and Drawing Angles and Triangles

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Explore:Example #1: Without using a protractor, identify each angle as acute, right or obtuse

Example #2: Write the angle that corresponds to the letters.


Measuring Angles

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1. Measure the angle.

a: _______

b: _______

c: _______

d: _______

e: _______

f: _______

2. Intersecting lines on an angle

Step 1: Draw a line. Mark a point on the line P.Step 2: Place the protractor on the line with the origin at P. Step 3: Mark the point at the angle measure you want (140)Step 4: Draw a line that passes through the angle mark and point P.

3. Choose the correct angle.

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4. Draw the angle shown.





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Angle RelationshipsExploreExample #1: Calculate these angle sums

a. 10 + 25 = ______b. 30 + 40 = ______c. 12 +28 = ______d. 20 + 30 + 40 = ______

Example #2: Predict the sum of four angles around any point P. _____ Calculate the angle sums to check your prediction.

Did you know…

Origami, the Japanese art of folding paper, uses transformations, parallel lines, linesegments, perpendicularbisectors and angle bisectors?

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Angle relationships

1. Determine the measure of ∠ABC. The sum of the angles in a triangle is ______°. So, ∠XYZ = ____° - (50° + 60°)= ____° - ____°= ____°

2. Use a protractor to name the angles.

3. Find the missing angle.

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Angle: _________ Angle: _________ Angle: _________

4. Determine the angles in each triangle.

1. ______2. ______3. ______4. ______5. ______6. ______7. ______8. ______

BONUS : $10 ClementBucks

Find the missing angles.

Angle: _______________ Angle: _______________





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8.4 Area of a Parallelogram

How can we calculate area of parallelogram? (textbook. 101-108)

An architect designs a stunning new building that defies previously conceived construction plans. The building’s main feature is the angled windows that extend over the ocean below. The suspension-effect is an incredible illusion. As he finishes the blue prints, the architect makes a plan to send to the window makers. Suddenly he realizes there is a problem. How can he give them the exact area of the window space so that he does not exceed his budget?

What is the area of the front of the building? How do you find the height and the base?

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(Creepy parallelogram videos: https://www.youtube.com/watch?v=Rpkjb4Tx844)

Special quadrilaterals: fun with straws.

- Some quadrilaterals have all sides equal.- Some quadrilaterals have 2 pairs of equal sides- Some quadrilaterals have 2 pairs of parallel sides

Explore

Example #1: Write the properties of these four quadrilaterals share: all sides equal, 2 pairs equal, 2 pairs of parallel sides.

A quadrilateral is a polygon with 4 sides.

A parallelogram is a polygon with 4 sides with opposite sides parallel and equal in length.

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https://www.youtube.com/watch?v=Rpkjb4Tx844

https://www.youtube.com/watch?v=Rpkjb4Tx844


a. _________ b. _________ c. _________ d. _________

Example #2: Check the properties of these parallelograms: all sides equal, 2 pairs equal, 2 pairs of parallel sides.

a.

_________

b. _________

c. _________

d. _________

e. _________

Example #3: How do you determine the area of a parallelogram?

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Step 1: draw a rectangle that is 6 x 4 cm on grid paper. Cut out the rectangle with scissors. Step 2: Count the number of square centimetres the triangle covers. What is the area of this rectangle?Step 3: Use scissors to cut across the rectangle diagonally, as shown above. Tape the two pieces together. Step 4: What shape did you form? What do you know about this shape that helped you identify it?Step 5: Is the area of the parallelogram the same as the original triangle? How do you know?Step 6: label the base and height on the parallelogram. What is the relationship between b and h, and the area of the parallelogram?

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Try it Out:1. Find the base and height of the shapes. Use a ruler.

2. Split the trapezoid into a triangle and a rectangle, then find the area of each shape in square units.

Time for a story about a story…

“Eureka! It all starts with this!” shouted Euclid of Alexandria, an extraordinary mathematician and generally enthusiastic young man. He was holding a branch above his head majestically.

“Just because you are the Father of Mathematics does not mean you can shout!” reminded the tutor. He was always annoyingly reminding Euclid of obsolete and obscure rules. In fact, the only thing that mattered to Euclid were mathematical rules. I mean, honestly, what else was there?

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“As I was saying,” Euclid continued, ignoring the old man. The branch was shoved in the tutors face, “The answer to everything! You see, the branch starts with a point, a singular dot! The laws of nature are but the mathematical thoughts of God!”

“Ah…yeah…”“And then it extends out…. I mean, think about it. It could just go

on and on and on and on and on…”“Euclid…”“And on. I’m brilliant! EVEYRTHING starts with a point. The only

thing that separates one thing from another thing is the direction the point takes.”

“Huh?”“Think about it. A branch is just two points. One at the beginning

and one at the end. Write this down in my little book there- “The Element.”

“The what?”“My axiom book- you know, that book I am writing about well

established rules that prove beyond a doubt that my theories is true.”“A big arrogant, but sure…”“So, as I was saying… point, line… oh yeah- so the line is really

just two points. And a circle is just a line that has one point, and a triangle has three points and a square has four points, and an octagon has EIGHT points. Everything, I mean, everything starts with a singular dot! Do you get the point?”

”Sigh. Yeah… I got the point…”

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Area of a ParallelogramBase (b) is 5cm and height (h) is 3 cm. Substitute the values into the formulas for the area of the parallelogram.A = base x heightA = b x hA = 5 x 3A = 15The area of the parallelogram is 15 cm.

Try it Out:1. Jessica is going to plant 10 tulips

per square meter. That means each square meter of her garden will have 10 tulips in it. The area of the garden is 40m2. How many tulips can she plant?

2. Dianna has enough parallelogram-shaped tiles to cover a section of wall with an area of 840cm2.The design will have a base of 12 cm. How high can her design go?

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Area of a Parallelogram

1. These parallelogram are drawn on centimetre grid paper. What is the area of each parallelogram?

a. _______ b. _______ c. ________ d. _______

2. Draw each of the following parallelograms. Use the formula to determine the area of each parallelogram. Check your answers using estimation.

a. b = 4cm, h = 5cmb. b = 3cm, h = 7cm

3. What is the area of each

parallelogram?

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a. A = _______ cmb. A = _______ m

4. Design a logo for a t-shirt with your initials. Use parallelograms. What is the area of your initial?

8.5 Area of a Triangle

How can we calculate area of triangle? (textbook. 109-115)

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Explore

Example #1: Without using a protractor, identify each angle as acute or obtuse.

a. _________

b. _________

c. _________

d. _________

e. _________

Example #2: Practice using the correct scale to measure angles.

Step 1: Estimate: is the angle acute or obtuse? Step 2: Place the origin of the protractor on the angle vertex Step 3: choose the correct angle measure.

The angle is obtuse or acute The angle is obtuse or acute

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The angle measures ___110°___ The angle measures ______

Example #3: Measure each angle.

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Try it Out:

How can you determine the area of a triangle?

Step 1: draw a rectangle that has a base of 6cm and a height of 4cm on grid paper. Cut out the rectangle with scissors.

Step 2: count the number of square centimeters. What is the area of the triangle?

Step 3: draw a diagonal line from one corner to another. Cut along the line. Tape the two pieces to make a rectangle.

Step 4: Predict the length and height of the new shape. Predict the area. What is the relationship between the b and h of the new shape and the area of the triangle?

1. This triangle has a base of 4cm and a height of 7cm. Determine the area.

A = base x height ÷ 2A = b x h ÷ 2A = 4 x 7 ÷ 2A =

2. Palliser’s Triangle has a base of approximately 760 km and a height of ~390 km. What is the area of the prairie land?


Area of a Triangle

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1. These traingles are drawn on centimeter grid paper. What is the area of each of the trinagles?

2. Draw each traingle on centimeter grid paper. Determine the area of each using the formula.

a. b = 6cm, h = 7cmb. b = 5cm, h = 4cm





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BONUS $10 ClementBucks

How much material is needed to make the two sails on this sailboat?

Would you need any additional material for the sails? Explain.

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8.6 Constructing CirclesHow can we draw circles with a given radius and diameter? (textbook. 268-272)

ExploreExample #1: The center of an arc is the point where you put the compass to draw an arc. Draw a circle at the point where the compass sits.

Example #2: Construct a circle with center O through point A.Step 1: Set the compass point on the center point, OStep 2: Adjust the compass width to point AStep 3: Draw a circle through point A

A circle consists of all the possible points that are the same distance from a point called the ________. The distance between any point and the center is called the _________.

An ______ is an unbroken part of a circle. The center of the circle is also the center of the arc.

A ___________ is a tool used to construct circles and arcs.

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Example #3: Construct an arc with center P through A.

Is point B on the arc? ____________

Example #4: The arcs are centered at points A and B. Use a compass to extend each arc into a circle. How many points of intersection do these circles have?

Two lines can intersect at 1 point or 0 points. Two line segments also can intersect a 1 or 0 points. Two arc of different circles ( or two circles, an arc and a circle) can intersect at 2, 1, or 0 points.

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Try it Out:

1. Use a compass to create a line segment CD equal to the line segment AB along the given line.

2. The center of the arc is point C. Construct a line segment AB equal to the radius of the arc.

Step 1: Set the compass to the radius of the arc.Step 2: Set the point of the compass on AStep 3: Draw an arc intersecting the line.

3. Mark any two points on one of the circles above. Label the

You can use a compass to create line segment CD equal to a line segment AB.

Step 1: set your compass to the width of AB.

Step 2: without changing the settings of the compass, put the point of the compass on C.

Step 3: Construct a little arc intersecting the line. Label the intersection D.

The diameter of a circle is the distance across the circle. It is measured through the center. The radius is half the diameter.

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points C and D. Construct a line segment OC and OD using a ruler. Measure them.

OC = ______OD = _____

Explain why OC = OD

4. Find the radius and diameter.

Radius: _____ Radius: _____ Radius: _____ Radius: _____Diameter: _____ Diameter: _____ Diameter: _____ Diameter: _____

5. Fill in the missing diameter or radius.

Radius 3 cm 4 cm 12 cm

38cm r

Diameter

6 cm 4 mm

12 m

1m 1.6cm

6. Draw and measure the diameter.

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Unit 8 Math Name: _________________

Mrs. Clement Teacher Check________________

Inquiry ProjectGo back to your sketches for the Soccer Field. Create a good copy. You must show evidence of using bisecting lines and angles. In other words, DO NOT ERASE YOUR LINES.

Use your knowledge of bisecting lines Use your knowledge of creating right angles Use your knowledge of parallel and perpendicular

lines

NOT SO GOOD GOODGREAT

Marking Rubric (assignment: /15)

1 2 3 4 Mark

Evidence of ruler, protractor and set triangle: Parallel line segments

/3

Evidence of compass and ruler: Perpendicular line segments

/3

Use of compass and protractor: angle bisector

/2

Sketch marks are present (not erased or drawn in afterwards)

/2

Details: handling of compass, neat lines with ruler, accurate angles, even lines, parallel lines.

/5

Unit 8 Math Name: _________________

Mrs. Clement Teacher Check________________ 8.7 Circumference of a CircleHow can we estimate and calculate the circumference of a circle? (textbook. 273-279

Squares4 equal sides

Width (w) = 1cmSide length = 1cmPerimeter (p) = __

P= 1cm x 4 = 4cmP : w = ____

w = 2 cms = 2 cm

P = ________P : w = _______

w = 3 cms = 3 cm

P = ________P : w = _______

Hexagons6 equal sides


P= 2cm x 6 = ___cmP : w = ____

w = 2 cms = 2 cm

P = ________P : w = _______

w = 6 cms = 3 cm

P = ________P : w = _______

Octagons8 equal sides


P= ____ x 8 = ___cmP : w = ____

w = 4 cms = 1.5 cm

P = ________P : w = _______

w = 12 cms = 4.5 cm

P = ________P : w = _______

Talk to the person next to you about what you have noticed about the ration of p to w in each row.


Explore:Example #1: What is the ratio of the circumference of the circle to its diameter (width)?

A. Measure the diameter (width) of the circles. Estimate the circumference of the circles by calculating the perimeters of the regular octagons.

B. Determine the ratio of the circumference to the diameter of each circle above. Then divide the circumference by the diameter to write each ratio in the form _____ : 1.

a. C:d = ___: ____ = ___: 1b. C:d = ___: ____ = ___: 1c. C:d = ___: ____ = ___: 1

The ratio of the circumference to the diameter

of the circle is about _______.

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Diameter (d) __22mm__Side of octagon __8mm__Perimeter __64mm_Circumference (c) _~64mm_

Diameter (d) ______Side of octagon ______Perimeter ______Circumference (c) ______

Diameter (d) ______Side of octagon ______Perimeter ______Circumference (c) ______


Example #2: Find the approximate circumference of circles with the given measurements. Use 3.14 for π.

a. diameter = 7mcircumference = π3.14 x 7m= ___________

b. diameter = 10mcircumference = ___________= ___________

c. diameter = 1.5 cmcircumference = π3.14 x ___________= ___________

8.7 Area of a Circle

The ratio of circumference to diameter is the same for all circles. The number has an indefinite number of digits after its decimal. Mathematicians use the Greek letter π (pronounced pi) to identify it.

π = 3.14

Circumference : diameter = π : 1

Reflection:

Which parts of circumference did you find pretty straightforward?


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How can we estimate and calculate the area of a circle? (textbook. 280-286)

ExploreExample #1: Estimate the area of the circle by finding the area of the shaded part.

a. Find the area of each shaded shape in the top right quadrant of the circle.

b. Add the areas in a) to get the area of a quarter of the circle. Area of the circle ~ _________

c. Find the area of the shaded part of the grid using answer in b). Area in the circle ~ ______________.

Example #2: The radius of the circle above is r = _____. Divide the area you found in Example 1 by r2. What do you notice: ______________ ____________________________________________________


Area of a Circle

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1. Find the area and the circumference around each figure.

a) A = _______ C= ________b) A = _______ C= ________c) A = _______ C= ________

2. The rim of a bicycle tire has a radius of 30cm. The tire is 5cm thick.

a. What is the radius of the outer circle of the tire?

b. What is the circumference of the tire?

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3. These two shapes are made from quarters or halves of circles and polygons. Find the area of the shapes.

4. A tractor wheel has a diameter of 1m. About how many times would the wheel turn if the tractor drove 100m?

5. The London Eye is a giant Ferris Wheel in downtown London, England.

a. The diameter of the wheel is 135m. What is the circumference of the wheel?

b. If the wheel turns 0.3m every second, about how long does it take for the wheel to rotate once?

Recap: What’s Going to Be on the Test?

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8.1 Parallel and Perpendicular Line Segments Draw a line segment with parallel lines Draw a line segment with right angles

8.2 Draw perpendicular Bisectors Draw a line that divides a line segment

8.3 Draw Angle Bisectors Draw lines that divide angles in half

8.4 Area of a Parallelogram Develop area formulas Calculate area of parallelogram

8.5 Area of a Triangle Develop formula for triangles Calculate area of triangle

8.6 Construct Circle Draw circles with given radius or diameter Determine diameter Determine radius

8.7 Circumference of a Circle Estimate and calculate circumference Solve equations

8.9 Area of a Circle How to determine area Estimate and calculate area Solve equations


BONUS BONUS $20 ClementBucks

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