Scale Diagrams, Enlargements and Reductions

Scale Diagram: ________________________________________________________

______________________________________________________________________

Corresponding Lengths: ________________________________________________

______________________________________________________________________

Scale Factor: __________________________________________________________

______________________________________________________________________

Enlargement: __________________________________________________________

______________________________________________________________________

Reduction: ____________________________________________________________

______________________________________________________________________

Proportional: __________________________________________________________

Here is a drawing of a rectangle and an enlargement of the drawing.

Actual Drawing

Scale Diagram

Measure the lengths of pairs of matching sides on the drawings.

Label each drawing with these measurements

For each measurement, write the fraction:

Write each fraction as a decimal. What do you notice about these numbers?

Examples:

1. This drawing of a minnow was printed on the page of the High River Journal. This minnow was going to be used by Chet Cooper to help catch some Jack (another type of fish). The actual length of the minnow was 3 cm. Determine the scale factor of the diagram.

15 cm

2. This photo of a bale of hay is 15 cm long by 9 cm wide. If a scale factor of 15/2 can be used, calculate the actual size of the bale

3. Draw a scale diagram of the yield sign. Use a scale factor of 3.5

2.5 cm 2.5 cm

3 cm

Here is a drawing of a rectangle and a reduction of the drawing.

Scale Diagram

Actual Drawing

Measure the lengths of pairs on matching sides on the drawings.

Label each drawing with these measurements

For each measurement, write the fraction:

Write each fraction as a decimal. What do you notice about these numbers?

4. Draw a scale diagram of this shape. Use a scale factor of 0.25.

12 cm

8.6 cm 8.6 cm

6 cm

Similar Polygons and Triangles

Similar Shapes: ________________________________________________________

______________________________________________________________________

Corresponding Angles & Sides: __________________________________________

______________________________________________________________________

Proportional Sides: _____________________________________________________

______________________________________________________________________

When one polygon is an enlargement or reduction of another polygon, the polygons are similar.

Similar polygons have the same _______________, but not necessarily the same ____________.

Matching angles are _____________________________ angles.

Matching sides are ______________________________ sides.

Properties of Similar Polygons

When two polygons are similar:

· Their corresponding angles are equal

· Their corresponding sides are proportional

Symbol: ~ “Similar to”

Examples:

1. Identify pairs of similar rectangles

N

J

B

A

5.25 cm

1.5 cm

2.4 cm

2.5 cm

8.4 cm

8.5 cm

D

C

F

E

K

M

G

H

2.

a) Using a scale factor of 1.5, what will the new dimensions be of a similar pentagon? Will the angles change?

a) Using a scale factor of 0.5, what will the new dimensions be of a similar pentagon? Will the angles change?

3. The two polygons are similar.

a) Calculate the length of GH

b) Calculate the length of NP

4.

Find the length of JK and ST if JKL ~ RTS

12

T

18

S

R

5

L

K

J

9

5. Determine the length of ST given the following information

P

210 m

305 m

T

S

R

Q

230 m

Reflections and Line Symmetry

Line of symmetry: ______________________________________________________

_____________________________________________________________________

Line of Symmetry is also known as _______________________________________

1. a) Which shapes have lines of symmetry? Which shapes do not?

b) If the shape does have lines of symmetry, how many lines of symmetry?

2. Identify the triangles that are related to the shaded triangle by a line of reflection. Describe the position of each line of symmetry.

100

D

C

8

10

8

6

4

2

6

4

2

B

A

3. Quadrilateral ABCD is part of a larger shape.

· Draw the image of the ABCD after each reflection below.

· Write the coordinates of the larger shape formed by ABCD and its image

· Describe the larger image and its symmetry

2

4

6

8

100

2

4

6

8

10

A

B

C

D

Point

Image

a) A reflection in the horizontal line

Through 2 on the y-axis

b) A reflection in the vertical line

2

4

6

8

100

2

4

6

8

10

A

B

C

D

Through 6 on the x-axis

Point

Image

c) A reflection in an oblique line

2

4

6

8

100

2

4

6

8

10

A

B

C

D

Through (0,0) and (6,6)

Point

Image

Rotations and Rotational Symmetry

Rotational Symmetry: ___________________________________________________

______________________________________________________________________

Order of Rotation: ______________________________________________________

______________________________________________________________________

Angle of Rotation Symmetry: ____________________________________________

______________________________________________________________________

Examples:

1. Determine which polygons below have rotational symmetry

State the order of rotation symmetry and the angle of rotation symmetry

Order of rotation: _______ ___________ _______

Rotational Symmetry:

Drawing rotation images

2.

Rotate the rectangle clockwise (CW) about vertex C. Draw the rotation image.

D

C

B

A

3.

Rotate the trapezoid ABCD counterclockwise (CCW) about vertex D

D

A

B

C

4. Rotate the rectangle EFGH. Draw an label each rotation image

i) 90o CW about vertex G

ii) 180o CW about vertex G

iii) 270o CW about vertex G

F

E

G

H

Identifying Types of Symmetry on the Cartesian Plane

Translation: ___________________________________________________________

______________________________________________________________________

Example: Translate the square 2 units right and 3 units down.

Review Line of Symmetry

Rotational Symmetry

Perform the following operations on the shape below

i) Translate rectangle ABCD 8 units right, 5 units up

ii) Rotate rectangle ABCD 90o counter-clockwise about the origin

iii) Reflect rectangle ABCD about the line y = 2

C

B

A

D

Similarities and Transformations Review Sheet

(check solutions at the end)

1. The dimensions of a picture of a minnow in the High River Times are 18 cm by 10 cm. An enlargement is to be made for a poster with dimensions 4.23 m by 2.35 m. What is the scale factor of the poster?

2. A scale diagram of each object is to be drawn with the given scale factor. Determine the corresponding length in centimetres on the scale diagram.

a)

Fishing rod length 280 cm, scale factor

b)Boogie board length 150 cm, scale factor 1.4

c) A racquet ball court length 10 m, scale factor 0.04

3. The scale diagram below has a scale factor of 0.25. What are the dimensions of the actual rectangle?

8 cm

2 cm

4. Which rectangles are similar? Give reasons for your answer.

5. These polygons are similar. Determine each length.

a)PT

b)BC

6. Identify the shapes that are related to the shape X by a line of reflection. Describe the line of symmetry in each case.

7. State the order of rotation and the angle of rotation symmetry for each. a)b)c)d)

Solutions:

1. Scale factor is 23.5

2. a) 5.6 cmb) 210 cmc) 40 cm

3. The dimensions are 32 cm by 8 cm.

4. A and C are similar. Both have a scale factor of 3.

5. a) 2.4 cmb) 5 cm

6.

A is a reflection at the line

B is a reflection at the line

C is not a reflection

D is a reflection at the line , OR using points (0,0) and (5,5) can use other possible coordinates

7. a) 2; 180ob) 4; 90 oc) 1; 360 od) 2, 180 o

length on scale diagram

length on actual size drawing

V

360

angle of rotation symmetry =

the order of rotation

°

360

°

90

°

90

°

50

1

4

x

=

7.5

y

=

yx

=

length on scale diagram

length on actual size drawing