a.

AWM1O Ch. 6 Getting Started Assignment

PART A: How to Cross Multiply

When we need to solve for a variable in a proportion, we have to cross multiply in order to solve for it.

Variable: an unknown value represented by a letter.

Steps to solve for a variable in a proportion:1) Multiply the variable with the number diagonal from it.2) Multiply the other 2 numbers that are diagonal from each other.

3) Divide both sides by the number in front of the variable (multiplied to it).

Examples:

7 10735

s_8 310

‘0192

Oldeea—(6

K,—C—

0!1

S0162r79

01*rIb

‘S96

:uopsodojipaAqo

PART B: How to simplify fractions and to put them into mixed numerals.

Mixed numeral: a whole number and a fraction together.

Greatest common factor: largest number that will divide evenly into 2 (or more) numbers.

Multiplying fractions: multiply the numerators and then multiply the denominators. Remember that a

whole number has a 1 as a denominator.

Examples:1)i2÷6= 2)÷8= 3) j2÷6=

18÷6=3 56÷8=7 42÷6=7

4)27—9=3 S)32—4=8=13/s 6)+5914/536 ÷9 =4 20 ÷4=5 20÷5=5

StnpN1 each. Vrte your aus\ver a a inked number when posib1e.

.6 .45i). 2)

12 93) 4) —.

32

4 12

I2 3O

320)45

36 :729) .—

l0 —

96 126

11) 12)30 •6

fl)8 42

15) 16)20

60 .. 361?) — 18)

96

‘0 3619) :. 20)

32 45

Some more practice...

Simplify co’h. Write your answer a a mixed number when possible,

iS 42

30 24

42 249) : 1O

Find eaeb product.

IL)}.9

13) 7! 14) 23

15) 10 16)

17) 2x’ U)

219) l2.j

20)

Name:

AWM1O Ch. 6.1 Similar Figures Notes

When two figures or shapes are similar, one figure or shape has dimensions (length and width) that are

proportional to the other figure. We will look at many different types of figures and determine whether

or not they are similar.

Similar Figures:

Congruent:

Corresponding Angles:

Corresponding Sides:

Example 1Debbie works at an art gallery and is adjusting a bear image to fit on a certain wall. She is not sure if she

changed the length and width by the same amount and wants to find out if she has used the right ratio for

each dimension.

a) What is the ratio of lengths (the horizontal measurement)?

b) What is the ratio of widths (the vertical measurement)?

c) Has the same ratio been used in both cases?

d) Are the two pictures similar?

Example 2

Steve and Tanya are moving from their home in Chilliwack to a new larger home in Hope. Tanya loves

her garden so much she wants to build a bigger one in Hope but keep it exactly the same shape. Steve

drew out the plans for the new larger garden on the right.

a) Are these two gardens similar?

Example 3A tissue company creates rectangular tissue with a length of 9 cm and a width of 10 cm. They want to

increase the size of their tissue for people with bigger noses by a factor of 1.7. What would be the new

dimensions of the larger tissue?

Let’s say the tissue company wanted to decrease the size by 2 for people with smaller noses. What would

be the dimension of the smaller tissue?

2O.4rn

Name:

AWM1O Ch. 6.1 Worksheet#1 Assignment

Each pair of figures is similar Find the missing side.

1) 2)

?2A

5) 6)

A

1aj

8)73

10)

7.862.4

<B=______

AB=

BC=

CD=

DA=

ARACDE — DF

AC = ED

L4=LD

AC - DEiC — EP

x

11. In the following pictures below write down all of the corresponding sides and corresponding angles

between the two shapes.w

B

12. Which property proves that zABC issimilar to ADEF?

‘C

A.

a

C

a

A lcni

I cm

B

F

E

13. If zRST is similar to zLMN and angle measures of ALMN are as follows,

what are the angle measures of zSRST? T

ZL=85° M=78° LN=17°

15. Staceyis bored and draws a scale drawing of her room. If the actual size of her longest wallA is

12.75’, what is the size of all of her other walls in real life. Use corresponding sides to solve for each wall.

WallA: 12.75’

Wall B:

_______

Wall C:

_______

Wall D:

________

Wall E:

________

14. Find the lengths of the smaller figure.

A. 21cm F

MA

LP=

______

op=

______

NO=

______

MN=_____

I p

=

r=ar

Wall F:

________

Name:

AWM1O Ch. 6.1 Worksheet#2 Assignment

Answer each question and round your answer to the nearest Whole number

.11) Santa Cniz and Johnstown are 84 ml fromeai± other. How far apart would citiesbeonamapthathasasealeofl in; i4mi?

1.3) A.rnaphasascaieoflcm:i2km. IfGreenwood and Rivertown are 9 cm apartan the map then how far apart are the realcities?

15) A particular giraffe is 16 taI1 A model ofitwasbuiltwithascaleoflm 811 Howtall is the model?

17) A6fttallmanstandingnexttoaladdcrcasts a 3 ft shadow If the ladder casts ashadow that is? ft long then how tall is it9

12) Amaphasascaleoflin: l6mi. IfSaataCniz. and Brisbane are 64 iiii apart then theyare bow far apart on the nap?

14) A model house is 6 in tall If it was builtwathascaleofirn 3fttbenhowtaflastheacal house?

16) Apartoulartrairis I2fttalL Amodeiafit.wasbuiltwithascaleoflin:4ft. Howtallis model?

18) ifa3fttallcarcastsa9ftiongshadowthenhow tall isa woman that casts a 18 ftshaw?

19) Astatuethatis 15fttallcastsasha*:lawthat 20) lfa8fttallbabygiraffecastsa4ftlongis 5 ft long. Find the length oi the shadow shadow then how long is the shadow that athataI8tIaduitgiraflecasts. 1fttaIl statue casts?

21) Franklin and Clayton are SC) km from each 22) Find the thstance between Rwertown andother, how far apart: would the cities be Cfl Yorkshire on a map with a scale oft cm: Samapthathasascaleofl cm: 10km? kmifthey areactuaflyl2kmapart

23) Rivertown and Abbots Rise are 2 in apart on. 24) Find the distance between Kumba andaniapthathasascaleofl in :lmi, How Midwayiftheyare5inapartonamapwith.far apart are the real cities? a scale of I in: 5 mi.

25) A model motorcycle has a scale of I in : S ft.If the real motorcycle is lOft long then howlong is the model motorcycle?

26. Two triangles are similar. One has sides of 8 m, 5 m, and 6 m. If the longest side of the second triangle is 5

m, what are the lengths of the other two sides?

27. A pentagon has interior angles of 108°, 204°, 630, 120°, and 45°. Rudy wants to draw a similar pentagon

with sides twice as long as the original. What size will the angles be?

28. Marie-Claude has a series of four nested funnels in her kitchen that are similar to the one shown in the

diagram. If the other three funnels have top diameters of 10cm, 8 cm, and 6 cm, find the measures of the

remaining parts for all three funnels.

a) Funnel Height:

_________________

1.

2. 16cm

3. /

b) Stem Height: 10cm

1.

2 cm

2.

3.

Name:

AWM1O Ch. 6.2 Determining if Two Polygons are Similar Notes

When we would like to determine if two shapes are similar we must check that their

________________

are the same as well as their

______________.

If these two things are not equal then the shape will not besimilar.

Review: Try to solve these in your head

x 30 5045 72108

10100 x — 9 x12

Scale Factor:

Example 1Are the following shapes similar? If so prove it

55cm 27.5cm:::r 9

20,5cm

41cmRcacdos Posier

Original Posior

What is the scale factor of Ricardo’s poster?

Example 2To the right are some cedar hats Aithea is designing in three different sizes

a) Are they the same shape?

J1\/45 45°\

Small Medium Large

b) Are they similar figures?

Example 3

Lionel Richie is building a model boat to “sail on down the line.” A model was constructed before the

actual build. The model is on the left and the real size is on the right. Are they similar? What is the scale

factor?

36” N

_________________________R

15 //15 25” ‘___/‘25”

“p 0”T 4” S

Example 4

Rhoniel is an interior decorator who is creating a wall pattern with similar parallelogram stencils. She

created the three similar parallelograms shown. She wants to make the corresponding sides of each

stencil have the same four colors: brown, yellow, blue, and orange.

a) Help Rhoniel list the pairs of corresponding B

_______________________

C

sides to figure out her paint colors. // //8 cm/’ \ cm

/ /// /115 cm

F/ 12 H/1

/

A /° /‘D \ //

b) What scale factor was used on ABCD to K I

create EFGH? izs° /

‘10cm

16cm M

c) What is the measure of side BC?

d) What is the measure of angle D?

e) What is the angle measure of <L? How do you know? Explain your Answer

Name:

AWM1O Ch. 6.2 Worksheet Assignment

1. Pierre drew two regular hexagons (6-sided figures with all sides equal in length). Are the two hexagonssimilar? Why or why not?

2. Frank enlarges a photo to poster size. The original photo is 4 inches by 6 inches. If Frank enlarges it to1 m by 1.5 m, will it be similar in shape to the original? (Hint: Draw a diagram)

3. Are the following shapes similar? Show your work to support your answer.

4. One cylinder has a radius of 25 cm and a height of 35 cm. Another cylinder has a radius of 30 cm and aheight of 40 cm. Are the cylinders similar? Show your calculations. (fill in the diagram)

A D

B

z

5. 2 cm on a map refers to 60 km in real life. If Chilliwack to Whistler is 191 km, how far would that be on

the map?

6. The scale on a map is 2.5 cm:500 m.a) What distance is represented by a 12.5-cm segment on the map?

b) How long would a segment on the map be if it represented 1.5 km?

lOin

7. Cohn states that the following two figures are similar, but Tai disagrees, saying that they don’t have

enough information. Who is right? Show your calculations.

5cmIBm

9 cm5cm

8. While he was at the pet food store, Jeremy saw three different sized dog mats. They measured 36

inches by 28 inches, 27 inches by 21 inches, and 24 inches by 18 inches. Are all the mats similar? Show

your calculations.

Name:

AWM1O Ch. 6.1-6.2 Worksheet Assignment

****please draw diagrams with all of your work****

1. On a blueprint, a room measures 2.75 inches by 1.5 inches. If 1 inch represents 8 feet, what will be thedimensions of the room?

2. Jason wants to build a model of his house. He will build the model using a scale where 5 cm represents2 m. If one room is 6.5 m long, 4.8 m wide, and 2.8 m tall, what will its dimensions be in the model?

3. Redo Question 2 by first determining a unit scale (the number of centimeters that represent 1 meter),then calculating length, width, and height for the model.

4. If a house is 40 feet long, 35 feet wide, and the top of the roof is 27 feet above ground level, what willthe corresponding dimensions be of a model built so that 1 foot is represented by 12 inch?

5. Theresa folds origami paper to make stacked boxes. The outer box is 12 cm by 8 cm by 4 cm. Theresawould like to make two smaller, similar boxes, each scaled down by 5% of the previous box. What arethe dimensions of the two smaller boxes?

6. Are the two pentagons shown below similar? If so, explain how you know. If not, explain what youwould need to know. (Angles marked with the same symbol are equal.)

.

) 6cm

Li

7. The scale on a map is 2.5 cm: 500 m.

a) What distance is represented by a 12.5-cm segment on the map?

b) How long would a segment on the map be if it represented 1.5 km?

8. Show whether a rectangular prism that is 6m X 10 m X 8m is similar to one that is 4m X 7m X Sm.

9. While he was at the pet food store, Jeremy saw three different sized dog mats. They measured 36 inchesby 28 inches, 27 inches by 21 inches, and 24 inches by 18 inches. Are all the mats similar? Show yourcalculations.

10. Gina drew a scale representation of a field (see Polygon C). For instance, she drew a line2.2 cm to represent the actual measure (20 m) of this side (AD). Gina needs to complete thedrawing of Polygon D so that both polygons are similar.

;_J!i__1D

/ 28m3.’ in /

/1

-———— cG

Poiygcii C Pulygon D

H

in

F

11. The two tents below are similar. What is the height of the smaller tent.

12. A small soccer field is to be enlarged, though its shape will stay the same. What will be the area

of the new field?I II IS S

2idiS IS II 5

I

(O :J

13. The scale on the neighborhood map on the next page shows that 1 cm on the map represents an

actualdistance of2.5 km.

a. On the map, Waltham Street has a length of 14 cm. Using the scale, what would be the length of the

actual street?

b. Matapan Street has an actual length of 25 km. Show your work to find the right length of the Street Ofl

the map. Then use a ruler to see if your calculation is correct.

Name:

AWMIO Ch. 6.3 Drawing Similar Polygons Notes

Sometimes when we are enlarging a figure we can look to the scale factor to let us know how much largeror smaller our new object will be drawn.

Scale Factor:

Scale Factor greater than 1 will

Scale Factor that is a fraction will

Example 1If you were to enlarge the figure below by a factor of 1.5, what would be the dimensions of the largerversion be. Include the side lengths and angle measurements.

4cm

3.5cm

Example 2Lauren illustrates “how-to” manuals that show customers how to assemble furniture. One of her coworkers went home sick, and she was given the following diagram of a triangular shelf and told toredesign it. The triangular face of the new shelf has one side length of 60 cm and is defined as a similartriangle.

Now Lauren has to figure out the dimensions of the rest of the triangle. She needs to figure out what scalefactor her co-worker used. Is there more than one triangle possible?

cm

Example 3Determine what scale factor was used to create the larger piece and use the scale factor to calculate themissing side lengths.

Example 4Use the ratio method to create a pentagon that has been scaled down by a factor of ½.

How could you make a shape that is 1/3 bigger than the one below.

Name:

AWM1O Ch. 63 Drawing Similar Polygons Notes

Sometimes when we are enlarging a figure we can look to the scale factor to let us know how much largeror smaller our new object will be drawn.

Scale Factor:

Scale Factor greater than 1 will:

Scale Factor that is a fraction (less than 1) will:

Example 1If you were to enlarge the figure below by a factor of 1.5, what would be the dimensions of the largerversion be. Include the side lengths and angle measurements.

Example 2Lauren illustrates “how-to” manuals that show customers how to assemble furniture. One of her coworkers went home sick, and she was given the following diagram of a triangular shelf and told toredesign it. The triangular face of the new shelf has one side length of 60 cm and is defined as a similartriangle.Now Lauren has to figure out the dimensions of the rest of the triangle. She needs to figure out what scalefactor her co-worker used. Is there more than one triangle possible?

Example 3Determine what scale factor was used to create thelarger piece and use the scale factor to calculate themissing side lengths.

Example 4Use the ratio method to create a pentagon that has been scaled downby a factor of ½.

61n4

a

6 in

B in b

How could you make a shape that is 1/3 bigger than this one.

Name:

AWM1O Ch. 6.3 Drawing Similar Polygons Assignment

1. Use graph paper to construct a figure similar to the one given, with sides that are 1/2 the length of theoriginal. Explain how you know that the corresponding angles are equal.

HL___

2. Draw and label the lengths of the sides of a rectangle that has a length of 8 cm and is similar to arectangle that has a width of 10 cm and a length of 20 cm.

3. Barbie’s house is 55 ft wide and 40 ft deep. A drawing of her property shows the house is 10 in wideand 7.3 in deep. What scale was used on the drawing?

4. Xavier is building a staircase using scale drawings. On the drawing, the height of one stair is 0.5 cm andthe depth is 0.9 cm. Xavier will use a scale factor of 40 to build the stairs. Calculate the height and depthof the stairs he will build.

5. The scale ratio (model: original) between two diagrams is 3:5. If one measure on the model is 45 mm,what was the measure on the original?

6. Simian has built two end tables. The second table is a slightly larger version of the first. Given thedimensions below, calculate what scale factor Simian used to make the larger table.

7. Find the missing angles and measures of the following diagram.

3cm

I 1ff

42cirir

4Scrn

8. A craft store uses small gift boxes to wrap purchases. They have one box that is 20 cm by 12 cm by 5cm. Another box is larger by a scale factor of 1.3. What are the dimensions of the larger box?

9. Draw a rectangular prism similar to the one shown below with sides that are 1/2 the length of theoriginal.

i cmcm

10. Hazuki made a kite with the dimensions shown below. She decided it would work better if it werebigger. If her new kite tail has a length of 49 cm, what scale factor did she use, and what are the kite’sother dimensions?

11. A sporting goods store has miniature versions of tents on display. A six-person tent is 12’longby10’wide. The miniature version has a length of 1 ½ inches.

a) What is the width of the miniature version?

b) What is the scale ratio (miniature:actual)?

AWM1O Ch. 6.4 Similar Triangles Notes

, -1 S

I \ I\ 259

i3ftI \

Rft

Example 1Are any of the following triangles similar?

a/840

Example 2Sven is designing a T-shirt and wants to use several triangles in her design. She drew triangle ABC below torepresent the triangular shape she wants to use in her design. The side lengths of the triangle are as follows:

AB 4

BC 5

AC 6

DC 2.5. and

EC=3B

Section 6.2 defined that two figures are similar if their corresponding sides are proportional to each other andtheir corresponding angles are the same. The same rules apply to triangles, but you can determine if they aresimilar by using even less information.

Two triangles are similar if one of the two following requirements istrue.

• Any two of the three corresponding angles are equal• One pair of corresponding angles is congruent and the

corresponding sides adjacent to these angles are proportional.

D

Find the length of ED.

Example 3Roberto and Marcos tie wires to either side of an artificial tree aspart of the set-up of a concert stage. They decide to attach thewires so that they both make a 350 angle within a right triangle.

Are the right triangles created by the wires similar triangles?

Example 4Given that MBC in similar to LRST, AB is 6 cm long, BC is 5 cm long, and RS is 8 cm long, find the length of asecond side in ARST. Can you find the length of the third side? Explain your answer.

Example 5Ravi notices that a 2-rn pole casts a shadow of 5 m, and a second pole casts a shadow of 9.4 m. How tall is thesecond pole? (sketch the situation)

Name:

AWM1O Ch. 6.4 Worksheet Assignment

1. Given the two triangles below, find the length of ii.

b) Are these triangles similar?

C

N

B

2. In each of the diagrams below, LABCis similar to LXYZ Find the length of the indicated side (to onedecimal place).

3. Gladis thinks that any two isosceles triangles will be similar. Use examples to prove or disprove herbelief.

An isosceles triangle

has two sides equal

in length, and two

angles of equal

measure.

aSi b

c 7 n

6.1

C

I

cC

8

4. Ethel notices that a 4-rn pole casts a shadow of 8 m, and a second pole casts a shadow of 22 m. How tallis the second pole? (please provide a diagram)

5. Midge has cut out two triangular shapes from a block of wood, as shown below. She says that the twoshapes are similar. Is she correct? Show your calculations.

6. Julian is visiting the Manitoba Legislative Building inWinnipeg, where he sees the statue of Louis Riel. Use theinformation in the diagram to find the height of the statue.Round your answer to the nearest whole number.

2 I

Sfta

AWM1O Ch. 6 Review Assignment

1. On a blueprint, a room measures 2.75 inches by 1.5 inches. If 1 inch represents 8 feet, what will be thedimensions of the room?

2. Jason wants to build a model of his house. He will build the model using a scale where 5 cm represents2 m. If one room is 6.5 m long, 4.8 m wide, and 2.8 m tall, what will its dimensions be in the model?

3. Redo Question 2 by first determining a unit scale (the number of centimeters that represent 1 meter),then calculating length, width, and height for the model.

4. Gina drew a scale representation of a field (see Polygon C). For instance, she drew a line to representthe actual measure (20 m) of this side (AD). Gina needs to complete thedrawing of Polygon D so that both polygons

PuIgou (. Pohoii Dare similar.

A 2! D

/7 1/

33rn1/ 28m

B33m

3an

4.4 cn

4.5cm

5. Find the missing angles and measures of the following diagram.

GF

1

42cm

6. Draw a rectangular prism similar to the one shown below with sides that are 1/2 the length of theoriginal.

7. The scale on a map is 2 cm: 600 m:.a) What distance is represented by a 16-cm segment on the map?

cm

b) How long would a segment on the map be if it represented 22 krn?

8. Zora says that the two rectangles below are not similar because 60/50 does not equal 100/30. Is Zoraright? Explain.

A 60cm

9. The lengths of the sides of a pentagon are 2”, 6”, 10”, 14”, and 24”. Calculate the lengths of the sides of asimilar pentagon if the shortest side is 5”. Draw a diagram

10. If a man casts a shadow that is 3.8 m long at the same time that an 8-rn flagpole casts a shadow that is15 rn long, how tall is the man? (draw a diagram)

100cm 30cm

0 C

Name: Block:_______ Date:

1. In order to show two figures are similar you must prove...?

2. The scale on a map is lcm:3km, how many cm on the map would 36 km be?

3. A picture of Carla’s pen in a magazine is 21 cm long, the real pen is 7 cm, what is thescale factor used to create the picture?

5. Picture two similar figures. One of the figures is 2 times the size of the other. If youcreate a similar shape that is 2 times as big, the angles will be...

3 x6. Solve the following: — —

5 35

7. What would the dimensions of this picture be if itwas enlarged by a scale factor of 1.75?

13GmAB E-. -

tOrn

7.2 m

AWM1O Ch. 6 Practice Test Test(30 marks)

4. In the picture below, what is the scale factor used to create Ricardo’s poster?a) 2

b)½

c) 3/4

d) 4

41cm

55cm

Original Poster

27.5cm

20.5cmL

RicardWs Poster

a) doubledb) tripled

c) the samed) halved

4cm

8. In the diagram, which side corresponds toside DC?

a)ADb) HGc) FGd) BC

11. Which of the right triangles below are similar?

F

1-C

Hiz

45 m

D

12. Which property proves that zXABC is similar to tXDEF?

AAB_ACDEDF

B. AC=ED

C. L4LD

D AC - DEBCEF

-7EV

/

/ •) cmD /

b

9. Determine what scale factor wasused to create the larger piece.

10. Which statement correctly expresses a similarity between two triangles in thediagram below?

E

a) AAGB-iCEDb) MGB —MCFc) MCFADEd) MFC —tIADE

C - -

---- 1

_____ ___

B

a) I and II onlyb) II and IV onlyc) I, II and III onlyd) II, III and IV only

Iv

2 cm

1 cm

4 cm D

13. A small soccer field is to be enlarged, though its shape willstay the same. What will be the area of the new field?

2 yd

60yd

II— —

PartB—shortanswersection;please showall your workforfullmarks1. The lengths of the sides of a pentagon (5 sided shape) are 2”, 6”, 10”, 14”, and 24”. Use scale

factors to calculate the lengths of the sides of a similar pentagon if the shortest side is 5”. (2marks)

2. Given that the two figures shown are similar, determine the values ofxandy (4 marks)

3. To determine the distance across a river (distance AB), Lila took the followingmeasurements. Assuming the two triangles in the diagram are similar, how wide is theriver? (2 marks)

8.5m

2EEJ

x

4. If a man casts a shadow that is 3.8 m long at the same time that an 8-rn flagpole casts ashadow that is 15 m long, how tall is the man? (2 marks)

5. Amin cut out two blocks of wood as indicated. Are the two blocks similar in shape? Roundyour final calculations to two decimal places. (2 marks)

6. Joanne knitted a blanket that measures 174 cm by 230 cm. Her sister asked Joanne to makea matching one for her son. If Joanne wants to make a similar blanket using a scale factor of0.55, what will its dimensions be? Include a diagram (3 marks)

7. In the following diagram, AB is parallel to ED, AB is 8 m, AC is 12 m, and CE is 7 m.Calculate ED to one decimal place. (2 marks)

7 In275 in

in

9.Zin

4 in

7 iii