2-d geometry - pbworksmsparvu.pbworks.com/w/file/fetch/80005358/chapter 7.pdf · 2-d geometry nel...

2-DGeometry

NEL 207

GoalsYou will be able to• describe properties of triangles

and quadrilaterals

• construct polygons usingmeasurement tools

• sort polygons according to linesymmetry and other properties

• communicate about polygons

Flying kites

07-NelsonMathGr6-Chap07 7/18/05 4:58 PM Page 207

The design is symmetrical.

The polygon

has at least one

obtuse angle.

The design has lots of acute angles.

The polygon has

an even number

of sides.

The polygon can be cut along a white line into two congruent polygons.

The design has some right angles.

208 NEL

CHAPTER 7

One of these polygons contains Chandra’s mystery design.

A. C.

B. D.

She made clue cards to help identify the mystery design.The yellow cards give clues about the polygon.The red cards give clues about the design on the polygon.

You will need• a transparent

mirror

• a protractor

• a ruler

G e t t i n g S t a r t e d

Mystery Design

? How can you identify the mystery design?

A. Describe each polygon. Which ones have the right number of sides to be the mystery polygon?

B. Are any other polygons eliminated by the yellow cards?Which ones? Why?

07-NelsonMathGr6-Chap07 7/18/05 4:58 PM 08

Do You Remember?

C. Are any other polygons eliminated by the red cards? Which ones? Why?

D. Which polygon contains Chandra’s mystery design?

NEL 209

A

E

D

C

B

1. Classify the following triangles two ways: first by angle measures and then by side lengths. Use the words obtuse, right, acute, equilateral, isosceles, and scalene.

a) c)

b) d)

2. Construct a triangle with a 73° angle between two sides with lengths of 3 cm and 5 cm.

3. Identify each angle in this polygon as acute, obtuse, right, or straight.


11CHAPTER 7CHAPTER 7

Estimating Angle Measures

210 NEL

Compare and estimateangle measures.

Denise is preparing for an air hockey tournament. She is working on shots on net that bounce off the side board once.

? At about what angle should a puck bounce off the side board to result in a shot on net?

Goal

You will need• a protractor

• a ruler

• an air hockey table model

Denise’s Sketches

I drew two sketches to show the path of the puck.

In each sketch, I show a dot where the puck starts andlines to represent the path of the puck.

I labelled the angles between the path of the puck and the side boards.

�A �B

F

Path ofthe puck


A. Denise says ∠A is about 45°. Do you agree? Explain. Test Denise’s estimate by measuring.

B. Estimate ∠B, ∠C, and ∠D. Test your estimates. What do you notice about the pairs of ∠A and ∠B, ∠C and ∠D?

C. If Denise bounces the puck off point F, about how muchshould ∠B decrease to result in a shot on net?

D. If Denise bounces the puck off point G, about how muchshould ∠D increase to result in a shot on net?

E. Choose a different point on the side board. Estimate an ∠E and∠F that will result in a shot on net. Test your estimate.

NEL 211

1. What strategies did you use to estimate the measuresof your angles?

2. a) What do you notice about the path of the puck if ∠E decreases?

b) What do you notice about the path of the puck if∠E increases?

3. What will happen if the puck hits the side board at aright angle?

ReflectingReflecting

Neither path results in a shot on net.

Communication TipAngles are noted usingthe “∠” symbol. Weread ∠A as “angle A.”

G

�C �D

Path ofthe puck

07-NelsonMathGr6-Chap07 8/3/05 9:56 AM Page 211


Investigating Properties of Triangles

212 NEL

Investigate angle and side relationships of triangles.

Khaled’s relay team is going to compete on a triangular course.Each runner runs one side length of the triangle. Khaled has one slow runner on his team. He thinks his team can win if the course has a short side for his slow runner.

Goal

You will need• a ruler

• a protractor

? How can you design a course so that Khaled’s team is more likely to win?

A. Draw some possible triangular courses. Include some thatare symmetrical and some that are not. For each course,make sure you follow the course rules.

B. Label each triangle so that the angles are labelled A, B, and C and the sides opposite them are labelled a, b, and c, in that order.

C. Measure the angles and side lengths for each triangle you draw.

D. Order the side lengths of each triangle from least to greatest.

Course Rules• total distance between

200 m and 250 m• angles between sides

are at least 40°• each side is at least

�14

� of the total

P

QR

p

qr

opposite sideIn a triangle, the side an angle does not touch.For example, theopposite side of ∠Q is q.


Mental Imagery

NEL 213

E. Order the angle sizes of each triangle from least to greatest.

F. Which of the courses you’ve drawn will best help Khaled’steam win?

1. How did you make sure that your courses met therequirements?

2. What strategy did you use to get the best course?

3. Compare the side length and angle size orders in Parts D and E. What do you notice?


You will need• a transparent

mirror

Visualizing Symmetrical ShapesThe coloured part of each drawing is �

14

� of a shape

that has a vertical and a horizontal line of symmetry.

A. Visualize the whole shape.

B. Draw your visual image of the shape.

C. Check that your drawing has both lines of symmetry.

Try These1. Complete each shape.

a) b) c)



Communicate About Triangles

214 NEL

Communicate and explain geometric ideas.

Emilio measured some triangles and noticed something trueabout all of them. He made a hypothesis.

? How can Emilio explain his hypothesis?

Goal

Communication TipThe plural of hypothesisis hypotheses.

hypothesisA statement that youthink you can test

A. Did Emilio state his hypothesis clearly?

B. Did Emilio communicate his hypothesis and his reasons using mathematical language?

C. Was it clear how Emilio would choose examples to test his hypothesis?

D. How can you improve Emilio’s communication?

Emilio’s Hypothesis

When I add the lengths of two sides of a triangle, the sum is always greater than the other length.I think this is always true.

I’ll test my hypothesis with more examples.

5 cm

4 cm

3 cm

5 cm

5 cm

5 cm

3 cm

4 cm2 cm

B

A

C

Communication Checklist

Did you use mathlanguage?

Did you explain yourthinking?

Did you include diagrams?�

�

�

Triangle A

2 + 4 > 5

2 + 5 > 4

4 + 5 > 2


21 m 18 m

8 cm

10 cm

13 mm

8 mm 8 mm

3 cm

7 m

Checking2. Raven noticed that in an isosceles

triangle, there seem to be two equalangles as well as two equal sides.a) What relationship do you notice

between the equal angles andthe equal sides in eachisosceles triangle shown?

b) Draw scalene triangles. Are any of the angles equal?

c) Write your hypothesis. Explainhow you could test it. Use theCommunication Checklist.

NEL 215

84° 84°

12°

68° 68°

44°

4 cm 4 cm

3 cm

6 cm

5 cm

5 cm

1 cm

5 cm

5 cm

74°

53° 53°

1. Why is it important to explain your hypothesis clearly?


Practising3. a) What do you notice about the number of lines of symmetry

in equilateral, isosceles, and scalene triangles?b) Make a hypothesis about the number of lines

of symmetry for these triangles based on your observation.

c) Test your hypothesis.d) Exchange your hypothesis with a classmate.

How can you improve on your partner’s communication?Use the Communication Checklist.

4. a) Calculate the sum of the two shorter sides of the triangle. Double the sum. Compare the doubled sum to the perimeter of each triangle. Make a hypothesis about this relationship.

b) Explain how you will test your hypothesis.


CHAPTER 7

F r e q u e n t l y A s k e d Q u e s t i o n s

216 NEL

Q: How can you estimate the size of an angle?A: You can compare it to some angles you know.

For example, ∠A is a little less than 45°, so it is probablyabout 40°. ∠B is between 60° and 90°, but closer to 60°. It’s probably about 70°.

Q: In a triangle, how are angle measures related to side lengths?

A: In a triangle, the largest angle is opposite the longest side,and the smallest angle is opposite the shortest side. Intriangles where angles are equal, the sides opposite theequal angles are also equal.

For example, the lengths of the sides of this triangle are 1.0 m,1.6 m, and 1.7 m. How can you label them without measuring?The smallest angle is 35°, so label the opposite side 1.0 m.The largest angle is 78°, so label the opposite side 1.7 m.Label the remaining side 1.6 m.

45°60°

90°

A

B

78° 67°

35°


LESSON

1

2

3

�

CHAPTER 7

M i d - C h a p t e r R e v i e w

NEL 217

1. a) Estimate the sizes of ∠A, ∠B, and ∠C.Explain your strategy.

b) Measure to check your estimates. How close were your estimates?

2. Trace the triangle. Without using a protractor or a ruler, labelthe side lengths and angle measures with these measurements.20° 60° 100°5.9 m 15 m 17 m

3. Irene was in a hurry when she measured some triangles and recorded these measurements. Identify possible errorsand suggest what she may have measured incorrectly.Explain how you know.a) 60°, 60°, 60° and 5 cm, 5 cm, 6 cmb) 80°, 80°, 20° and 5 cm, 5 cm, 1.7 cmc) 80°, 80°, 20° and 4 cm, 5 cm, 6 cm

4. Trade your answers for Question 3 with a partner. How could you improve on your partner’s explanations?

A

BC


Rebecca’s Diagram

The set designer gave me this incomplete sketch of a parallelogram.

My paper is not big enough for me to draw a diagram with side lengths in metres.

I’ll draw with a scale of 1 cm represents 1 m. Then I can draw in centimetres instead of metres.

I start by drawing and labelling the 5 cm side.

Then I construct the 110° angle at one end of the side. 110° is 20° past the 90° angle mark.


Constructing Polygons

218 NEL

Construct polygons based on angle measuresand side lengths.

The students made measurements for props to be built for aschool play. Rebecca’s job is to construct accurate scalediagrams of the props for the builder.

? How can you draw the scale diagrams?

Goal


• a protractor

Communication TipWhen a shape isconstructed, it isdrawn carefully withappropriate tools,such as rulers andcompasses, to meetthe requirements ofthe task. “Draw” oftenmeans “construct.”

parallelogram

110° 70°

5 m

4 m 4 m


NEL 219

1. In what order would you draw the sides and angles of a parallelogram?

2. In what order did you draw the sides and angles of the kite in Part C? Why does this order make sense?


kiteA quadrilateral that hastwo pairs of equal sideswith no sides parallel

kite

8 m

5 m

95°60°

110°

A. Draw and finish Rebecca’s parallelogram.

B. Measure the angles that were not given in the sketch.

C. Draw a scale diagram of this kite. Use a scale of 1 cm � 1 m.

I draw the 4 cm side.

At the other end of the 5 cm side, I construct the 70° angle and another side of 4 cm.

07-NelsonMathGr6-Chap07 8/3/05 9:57 AM Page 219

parallelogram

90° 90°

6 cm

11 cm

parallelogram

7 cm

regular pentagon

108°

5 cm

Checking3. Draw this polygon. Use a scale of 1 cm represents 1 m.

Measure and label the unlabelled sides and angle.

Practising4. Draw these polygons.

a) b) c)

5. Draw a rhombus with side lengths of 10 cm and anglemeasures of 40° and 140°.

6. The measurements of the sides and angles in thisparallelogram are all correct, but the set designer put some of the labels in the wrong places.a) What possible errors were made in this sketch?

Explain.b) Draw a scale diagram of the parallelogram.

220 NEL

parallelogram

28 m

28 m

125° 55°

125° 55°

21 m

21 m

100°

110° 60°

8 m

5 m

quadrilateral


Curious Math

NEL 221

Folding Along Diagonals You will need• quadrilateral

shapes

• a ruler

• a protractorTom’s folding

I notice that if I fold along this diagonal line I have two congruent triangles as halves.

But if I fold along this diagonal line then I get two different triangles.

Draw and cut out adifferent quadrilateral. Fold it along itsdiagonals. Determineif the halves arecongruent triangles.

Repeat with otherquadrilaterals. Record your results.

What are the characteristicsof quadrilaterals that givecongruent triangles whendiagonals are folded?

311 665544333322

11111 6655443322211 665544332222



Sorting Polygons

222 NEL

Sort polygons by line symmetry.

Kurt has a kite collection. He says that �13

� of his kites haveexactly four lines of symmetry.

Goal


• scissors

• polygon shapes

• a transparentmirror

? Which of the kites have four lines of symmetry?

Ayan’s Sorting

I’ll trace and cut out these polygons.

I’ll use a mirror to determine the lines of symmetry.

Then I will check by folding on the lines of symmetry.

I’ll sort the polygons by the number of lines of symmetry.

I’ll put the ones with four lines of symmetry together.


A. Trace and cut out Kurt’s kites.

B. Identify and label the lines of symmetry. Use a mirror.

C. Record the number of lines of symmetry of each polygon.

NEL 223

1. What clues did you use to help you locate shapes withfour lines of symmetry?

2. Were there any polygons with more sides than lines ofsymmetry? Were there any polygons with more lines ofsymmetry than sides?

3. For regular polygons, how can you quickly predict thenumbers of lines of symmetry?


Checking4. Sort Kurt’s kites according to number

of lines of symmetry and number of equal sides. Use a Venn diagram.

Practising5. a) Identify the lines of symmetry of each of these polygons.

b) Sort the polygons. Use the Venn diagram from Question 4.

6. Predict the number of lines of symmetry for a regulardecagon (a polygon with 10 sides). Show your prediction in a sketch.

At least 4equal sides

More than1 line of

symmetry

Sorting Kites



Investigating Properties of Quadrilaterals

224 NEL

Sort and classify quadrilaterals by their properties.

Qi created a poster about quadrilaterals for the bulletin board.

As he drew them, he noticed that some had diagonals that intersected at 90° angles and some didn’t. He also noticed that some had diagonals that were equal and some didn’t.

He made a hypothesis.

? How can you test Qi’s hypothesis?

A. Construct quadrilaterals with unequal diagonals to test Qi’s hypothesis. Use two straws of different lengths as the diagonals. Use the ends of the straws as vertices.Draw each quadrilateral. Include the diagonals in your drawing.

Goal

You will need• a protractor

• a ruler

• straws

Diagonals in quadrilaterals

parallelogram rectangle

kite trapezoid

square rhombus irregular

quadrilateral

Squares have

• equal diagonals

• diagonals that meet at 90°


B. Describe each quadrilateral. Are any of your quadrilateralssquares?

C. Construct quadrilaterals with equal diagonals to continue totest Qi’s hypothesis. Use two straws of equal length as thediagonals. Use the ends of the straws as vertices.Draw each quadrilateral. Include the diagonals in your drawing.Measure the angles where the diagonals meet.

D. Describe each quadrilateral. Are any of your quadrilateralssquares?

E. Is every quadrilateral that has equal diagonals and diagonalsthat meet at 90° a square? Explain using an example.

F. How can you improve Qi’s hypothesis?

NEL 225

1. What do you notice about the angles created where the diagonals meet in all of the quadrilaterals you constructed?

2. a) What kinds of quadrilaterals were you able to makein Part A?

b) What kinds of quadrilaterals were you able to makein Part C?

3. Make a hypothesis to describe the diagonals of eachkind of quadrilateral.



LESSON

1

2

4

�

CHAPTER 7

S k i l l s B a n k

226 NEL

1. a) Estimate the sizes of ∠A and ∠B.b) Explain what angles you used to help you estimate.

Give reasons for your choice of angles.c) Measure and check your estimates for ∠A and ∠B.

2. The triangle’s angles measure 110°, 20°, and 50°. The sideshave lengths 4 cm, 9 cm, and 11 cm.a) Trace the triangle.b) Label the angles and side lengths without using a

protractor or a ruler. Explain your reasoning.

3. Isaac’s measurements for the angles for these triangles are:60°, 35°, 60°, 90°, 55°, and 60°.a) Trace the triangles.b) Label the angle measures without using a protractor.

Explain your reasoning.

4. Construct a regular hexagon with side lengths of 8 cm and angle measures of 120°.

BA

Y

X

Z

A

B C Q R

P


4

5

6

�

5. Construct a parallelogram with the following measures:angles: 120° and 60°, sides: 4 cm and 6 cm.

6. Trace and cut out these polygons.a) Identify and label the lines of symmetry.b) Sort the polygons according to the number of lines

of symmetry.

7. A regular polygon has eight lines of symmetry.a) Sketch the polygon.b) Draw the lines of symmetry.c) Was the polygon you sketched the only possible

polygon? Explain.

8. What properties do the diagonals of these quadrilateralshave in common?

a)

b)

c)

NEL 227


LESSON

1

4

5

6

�

square rhombus

trapezoid hexagon

parallelogram

rectangle

CHAPTER 7

P r o b l e m B a n k

228 NEL

1. A puck bounces off the side of the air hockey game as shown.Selina estimates both the blue angles to be 50°. How canshe know, without measuring, that her estimate is close?

2. a) Construct 3 different quadrilaterals where three of theside lengths are 3 cm, 6 cm, and 8 cm.

b) Were any of the shapes rectangles? Explain.c) What’s the longest fourth side you made?d) Could you have made one with a fourth side of 20 cm?

Explain.

3. A polygon has been folded in half twice to make this rectangle.a) What could the original polygon look like?b) Is there more than one answer? Explain.

4. Which polygons could the clues refer to? Explain your answers.a) My number of lines of symmetry is equal to the

number of sides. Who am I?b) I have two pairs of parallel sides. My diagonals are

perpendicular, but they are not equal. Who am I?c) I have two pairs of parallel sides. I have two

obtuse angles. My diagonals are not perpendicular. Who am I?

78°

07-NelsonMathGr6-Chap07 7/18/05 5:03 PM 8

CHAPTER 7

F r e q u e n t l y A s k e d Q u e s t i o n s

NEL 229

Q: How can you construct a parallelogram when you knowits angle sizes and side lengths?

A: Start by constructing one side. For example, if the sides of theparallelogram are 7 cm and 4 cm, draw the 7 cm side.

Then draw the angles on eitherend of it. For example, if theparallelogram has 110° and 70° angles, then measure those angles. Make the two new sides the right length.

Draw the last side. Check thatthe last angle is correct bymeasuring. Label the measuresof all the sides and angles.

Q: How are the number of lines of symmetry of a regular polygon related to the number of sides?

A: The number of lines of symmetry of a regular polygon is the same as the number of sides.

Equilateral triangles have three sides and three lines of symmetry.Squares have four sides and four lines of symmetry.Regular pentagons have five sides and five lines of symmetry.Regular hexagons have six sides and six lines of symmetry.

7 cm

7 cm

4 cm 4 cm

110° 70°

7 cm

7 cm

4 cm 4 cm

110°

110°

70°

70°


LESSON

1

2

3

�

CHAPTER 7

C h a p t e r R e v i e w

230 NEL

1. a) Trace triangle ABC. Estimate its angles without using a protractor.

b) Which angles could you have used to estimate theseangles? Explain why these angles are good choices.

2. The side lengths of triangle ABC in Question 1 are 16 cm,27 cm, and 30 cm.a) Label the side lengths without using a ruler.b) Explain how you know how to label the side lengths.

3. a) The side lengths of this right triangle are 3 cm, 4 cm,and 5 cm. How would you label the side lengths withouta ruler? Explain your strategy.

b) Measure to check.

4. a) Measure the angles in these right triangles.b) Make a hypothesis about the value of the

sum of the two smaller angles. Use mathematical language.

B

A

C

53°

90° 37°

A

B

D

C


4

5

6

�

5. The side lengths of a parallelogram are all either 6 cm or 3 cm. Two angles measure 110° and 70°. Construct aparallelogram that matches this description.

6. a) Construct a scalene triangle that has an obtuse angle.b) Construct a quadrilateral with a 50° angle, a 95° angle,

and a side that is 4 cm long.c) Construct a regular pentagon with side length of 4 cm

and angle measure of 108°.

7. Order these polygons from least to most lines of symmetry.

8. Sketch at least three polygons for each description. If a polygon is not possible, explain why.a) a regular polygon with at least four lines of symmetryb) a regular polygon with six lines of symmetryc) a polygon with fewer than four lines of symmetry

9. Sort these quadrilaterals using a Venn diagram. Choose categories from the Properties list.

NEL 231

A

B

C

D

E

F

AB

D

EG

F

C

H

Properties• equal diagonals• perpendicular

diagonals• diagonals all

inside the shape


CHAPTER 7

C h a p t e r T a s k

232 NEL

Furnishing a BedroomThis is a bird’s-eye view of a bedroom.As the designer, you will choose furniture for the room.

? How can you furnish the bedroom?

Represent the top view of the furniture. Use polygons.

A. Draw the bedroom. Use a scale of 4 cm � 1 m.

B. Mark the door, windows, and closets.

C. Construct polygons to represent furniture whose top views match the guidelines.

D. Draw or paste the polygons on the diagram of the bedroom.

E. Explain how your selections meet the guidelines by labelling each polygon with its properties.

2 m

1 m

1 m

5 m

3 m

1 m1 m

closetdoor

windows

Task Checklist

Did you include a labelleddiagram?

Are your explanations clearand complete?

Did you use math language?�

�

�

Guidelines forfurnishing the room:• Include at least three

shapes with more thanone line of symmetry.

• Include a shape withmore than five lines of symmetry.

• Include shapes thatcontain angles ofabout 20°, 40°, and 120°.

• Include a shape withdiagonals that meet at a right angle.

• Include at least threeshapes with diagonalsthat are not equal in length.


CHAPTERS 4–7

C u m u l a t i v e R e v i e w

NEL 233

Cross-Strand Multiple Choice1. The highest mountain on Earth is Mauna Kea, Hawaii. Its

height from the floor of the ocean is 10 203 m, but 6033 m ofit is below the ocean. About which height is above the ocean?A. 16 236 m B. 4000 m C. 3000 m D. 16 000 m

2. In St. John’s, Newfoundland and Labrador, the precipitation isgenerally 0.135 m in January, 0.125 m in February, and 0.117 min March. Which is the total precipitation for these months?A. 0.377 m B. 0.477 m C. 0.367 m D. 0.387 m

3. In the 2004 Olympic Games, Emilie Lepennec of Franceplaced first in the final women’s uneven bars with a score of 9.687. Svetlana Khorkina of Russia placed eighth with ascore of 8.925. Which is the difference between the scores?A. 1.762 B. 18.612 C. 0.762 D. 0.562

4. Which unit is most appropriate to measure the thickness of a string?A. millimetres C. metresB. centimetres D. kilometres

5. Which would you measure in metres?A. the distance between cities C. the height of your deskB. the perimeter of the gym D. the length of a pencil

6. The largest recorded snail is an African giant snail thatmeasured 0.393 m in length. Which length equals 0.393 m?A. 393 cm B. 39.3 mm C. 3.93 cm D. 393 mm

7. Angele drew a parallelogram with a perimeter of 18.4 cm. Thelength of one side is 4.5 cm. Which is the length of another side?A. 13.9 cm B. 9.4 cm C. 4.7 cm D. 4.6 cm

8. Which number is a prime number?A. 61 B. 42 C. 21 D. 51

9. The distance between Ottawa and Edmonton is 3574 km.Jacob drove this distance 54 times last year. Which is thetotal distance Jacob drove between these cities?A. 32 166 km C. 182 996 kmB. 321 660 km D. 192 996 km


At least threeequal sides

More thanthree

lines ofsymmetry

Sorting Polygons

234 NEL

10. 63 students are sharing the cost of a school trip equally. Thetotal amount is $5607. Which is the cost for each student?A. $9 B. $809 C. $89 D. $80

11. Kurt drew a triangle with side AB 6.2 cm, BC 3.1 cm, andAC 4.5 cm. Which is true for the triangle?A. The triangle has one line of symmetry.B. The angle opposite AB is the largest angle.C. The triangle is isosceles.D. The angle opposite BC is the largest angle.

12. Which is the measure of the largest angle in this quadrilateral?A. 125º C. 130ºB. 100º D. 115º

13. In which place does this polygon belong in the Venn diagram?A. only the circle labelled: More than three lines of symmetryB. only the circle labelled: At least three equal sidesC. the overlapping section of the circlesD. outside both circles

14. Which is not true about a rhombus?A. It can have two acute angles and two obtuse angles.B. The diagonals are always equal.C. It always has four equal sides.D. The diagonals always meet at 90º.


NEL 235

Cross-Strand Investigation

FarmingDenise and Khaled are planning a booth about farming inOntario for a fall fair.

15. a) Denise read that in 2001, there were 59 728 farms inOntario, 53 652 in Alberta, and 21 836 in British Columbia.About how many farms were in these three provincesaltogether? Explain your reasoning.

b) About how many more farms were in Ontario thanBritish Columbia in 2001? Explain your reasoning.

c) Ploughing competitions are organized by the OntarioPlowman’s Association. A requirement for the match is thateach furrow must be at least a specific width. What unit isappropriate for measuring the width of a furrow? Explain.

d) What unit is appropriate for measuring the distance atractor is driven to plough four large fields? Explain.

e) Khaled found out that in 2002, Ontario farms produced810 t of fresh plums, and 26 times that amount ofpeaches, pears, and plums altogether. What was thetotal mass for peaches, pears, and plums?

f ) Denise measured two quadrilateral fields. In each field, the opposite sides are equal. The diagonals of the cornfield are equal, but they do not intersect at 90º. Thediagonals of the hay field are not equal, and do notintersect at 90º. What kind of quadrilateral is each field?Sketch diagrams to show your answer.

16. a) Denise did research on the number of farms in Ontario.She recorded the data in this chart. Round the numberof farms to the nearest thousand. Create a graph withthe vertical axis labelled Thousands of farms. Justify your choice of graph.

b) Khaled found data about farm operators on the Internet. He recorded the data in thischart. Write a fraction and a decimal todescribe each age group. Write each decimal in expanded form.

Farms in Ontario

NumberYear of farms

1981 82 448

1986 72 713

1991 68 633

1996 67 520

2001 59 728

Ontario Farm Operators by Age for Every 1000 in 2001

Number forAge group every 1000

Under 35 years 106

35–54 years 519

55 years and over 375


236 NEL

Cross-Strand Investigation

4-H ProgramsChandra and Rodrigo researched information about the 4-Hprogram for the fall fair. 4-H stands for Head, Heart, Hand, and Health. It is mainly a program for youths in rural areas, but people in urban areas also join.

17. a) Rodrigo met members of a 4-H club who visited a maplesyrup farm and brought home 10 L of maple syrup. Theyused 2.650 L of maple syrup for a squash and carrotsrecipe and 1.585 L for muffins. How much maple syrupdo they have left?

b) Chandra met members of a 4-H club who are making a quilt.Draw a rectangle patch and a scalene triangle patch, eachwith a perimeter of 16.4 cm. Label the length of each side.

c) Draw a rhombus quilt patch with side lengths of 5 cm andangle measures of 45° and 135°. Draw the lines of symmetry.

d) Chandra talked to members of a 4-H club who are growingpumpkins. The masses of their largest pumpkins were5.803 kg, 3.275 kg, and 4.006 kg. What is the total mass of the three pumpkins?

e) Each of the 22 members of a 4-H club decided to e-mail187 people from Alberta they met at a conference. Howmany e-mails did they send?

f ) What unit is appropriate for measuring the distancebetween Alberta and a 4-H club house in Ontario?

g) Chandra researched these data about 4-H clubs. Chandra says that the mean number of projectscompleted by a club is about 13. Do you agree?Justify your answer.

18. a) In Canada, 4-H started in Roland, Manitoba in 1913. Write a pattern rule for the 10th, 20th, 30th, …anniversaries. What are the 1st term and the commondifference? What year is the 100th anniversary? Use your pattern rule.

b) Create a survey question about projects that students in your class might like to do in a 4-H club.

c) The 4-H Ontario Magazine is mailed three times a year. Ina recent year, 109 648 magazines were mailed altogether.Write the number in expanded form in two ways.

Ontario 4 H Clubs in 2004

Members 6619

Clubs 934

Projects 12 412


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