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:
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______________________________________________________________________
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