1
Section 7.1 Scale Diagrams and Enlargements
A diagram that is an enlargement or a reduction of another diagram is called a scale
diagram.
Example #1:
Scale Factor=
length on scale diagram
length on original diagram
Scale Factor =
Note:
 the units must be the same on the original and scale diagram
 if not, you must convert one to make them the same
 scale factors do not have units
2
Example # 2
The cylinder is to be enlarged by a scale factor
of 25 . Find the dimensions of the enlargement.
Write the scale factor as a decimal.
5
2

Diameter Original:
Diameter Enlargement:
Height Original:
Height Enlargement:
The enlargement has diameter _______ and height _______.
Example #3:
A photo has dimensions 10cm by 15cm.
Two enlargements are to be made with each scale factor below.
Find the dimensions of each enlargement.
A) scale factor 4
Original Width:
Enlargement Width:
Original Length:
Scale Length:
Enlargement has dimensions _____cm by
B) scale factor
____cm
13
4
Original Width:
Enlargement Width:
Original Length:
Scale Length:
Enlargement has dimensions _____cm by
____cm
Complete: Pages 323 – 324 #’s 4, 5, 6, 7, 8, 11
3
Section 7.2 Scale Diagrams and Reductions

A scale diagram can be smaller than the original diagram.

This type of scale diagram is called a reduction.

A reduction has a scale factor that is less than 1
Example # 1
Scale Factor=
Diameter on Scale Diagram
Diameter on Original
Scale Diagram (d = 4cm)
Original (d = 10cm)
Example # 2
A top view of a patio table is 105cm by 165cm.
A reduction is to be drawn with scale factor 15 .
Find the dimensions of the reduction.
Write the scale factor as a decimal: ______
Original Length:________
Reduction Length:_______
Original Width:________
Reduction Width:_______
Dimensions of the reduction are ______ by ______
Proportion
An equation, such as
3
4
 86 , which states that 2 ratios are equal.
Two diagrams are “proportional” if all sides are multiplied or divided by the same number.
4
Example #3
Which diagram has sides that are
proportional to the original?
Diagram Length
Original Length
Diagram Width
Original Width
Are They
Proportional?
A
B
C
Complete: Pages 329-330 #’s 5, 6, 7, 8, 9, 11, 12
5
Practice
Enlarge the rectangle, triangle and arrow by a scale factor of 2. Enlarge the H by a scale
factor of 3.
Reduce the rectangle and triangle by a scale factor of ½ .
6
Use a scale factor of 3 to draw an enlargement of this letter K.
7
Section 7.3 Similar Polygons


A Polygon is a closed shape with straight sides.
Exactly 2 sides meet at a vertex (point).

When one polygon is an enlargement or reduction of another polygon, we say the
polygons are similar.

When 2 polygons are similar:
 matching angles are equal AND
 matching sides are proportional
Example # 1
Determine whether or not these polygons are similar.
Check the matching sides
All scale factors are equal, so matching sides are proportional.
These figures are similar.
8
Example # 2
The following figures are similar. Determine the length of JI and JF.
Determine the scale factor:
𝐻𝐼
𝐶𝐷
=
Multiply the corresponding sides in the original by the scale factor.
 JI corresponds with ED : JI =
 JF corresponds with EA : JF=
Example # 3: Cross Multiply Method
Find the length of zy.
ST VU
=
WX ZY
Complete: Pages 341-342 #’s 4, 5, 6, 7, 11
9
Investigation of Conditions for Similar Triangles
Complete the following tables:
ΔABC
AB
BC
AC
DE
EF
DF
Side Length
ΔDEF
Side Length
Calculate the following ratios to one place after the decimal point.
Is ΔABC~ ΔDEF? How do you know?
10
Complete the following tables:
ΔABC
A
B
D
E
C
Angle Measure
ΔDEF
F
Angle Measure
What do you notice about the angle measures in the two triangles?
Suggest two ways you may tell if triangles are similar.
11
Section 7.4 Similar Triangles
Two triangles are similar if they have the same shape, but different size.
In similar triangles:
matching angles are equal
matching sides are proportional
When writing proportions for corresponding sides, make sure to keep the same triangle on
top in each fraction.
P 
Q 
R 

Write a proportion that includes only 1 unknown. Cross multiply and divide to solve.
12
Example #2
Identify the 2 similar triangles and determine the missing sides.

P 
Match the corresponding angles Q 
M 

Write the similarity statement:

Write a proportion that includes only 1 unknown. Cross multiply and divide to solve.
Example # 3
Identify the similar triangles and identify the missing measures.
Complete: Pages 349 - 350 #’s 4, 5, 6
13
Similar Triangles & Word Problems
Example 1:
The length of a monument's shadow is 20.5m, when the length of Joan's
shadow is 4.1m. If Joan is 1.2m tall, calculate the height of the monument.
Example 2:
To measure the width of a river the measurements shown were made by a
surveyor. How will she determine the width of the river?
14
Example 3:
One triangle has two 500 angles. Another triangle has a 500 angle and an
angle. Could the triangles be similar? Explain.
Example 4:
Use the diagram below to answer the following questions.
P
Q
R
S
T
a). Which two triangles are similar? How do you know?
b). If PQ = 8.2 cm, QS = 5.3 cm and ST = 7.3 cm, find the length of RS.
Complete: Pages 350 – 351 #’s 7, 9, 11, 12, 14, 15
800
15
Similar Triangle Practice
4m
6m
1.5 m
1. Chris sights a rock across a river and walks along one of
the river banks making the measurements shown in the
R i v e r
diagram. How many metres wide is the river?
2. Sam, who is
1.7 m tall, casts a shadow of 3 m .
Rock
Calculate the approximate height of a tree in metres
if the tree casts a shadow of
25 m at the same time
25 m
of day.
Sam
3. A flagpole’s shadow is 15.5 m long at the same time John’s shadow is 3.6 m
long. If John is 1.8 m tall, what is the height to the nearest tenth of a metre
of the flagpole?
F
C
4. In the diagram shown, CBA ~ FED , AC = 8,
FE = 22 and CB = 4. Find DF.
A
B
E
D
5. A lighthouse’s shadow is 46.2 m long at the
same time that a tree’s shadow is 14.6 m long. If the tree
is 5.1 m, what is the height of the lighthouse to the
nearest tenth of a meter?
6. If  ACE BCD, find the value of x.
A
B
x
3
E
12
D
4
C
7. John wants to find the height of the light of a
local lighthouse. He stands so that the top of
his shadow falls on top of the shadow of the
lighthouse, producing the measurements shown
1.7 m
3m
in the diagram shown to the right. How tall is the lighthouse?
24 m
3m
16
Section 7.5 Reflections and Line Symmetry
The Taj Mahal is a famous example of
symmetry in architecture.
Many parts of the building and grounds were
designed and built to be perfectly
symmetrical.
Symmetry creates a sense of balance.
Line Symmetry
 a figure is divided into 2 congruent parts using a line of symmetry (mirror image)
 one half of the figure is reflected exactly onto the other half
 a figure may have more than one line of symmetry
The line of symmetry (also called line of reflection) can be:
 Horizontal (-----)
 Vertical ( | )
 Oblique ( / )
Is the dashed line in each figure a line of symmetry? Explain.
Is each a line of symmetry for the hexagon?
Can any more lines of symmetry be drawn for a hexagon?
17
Investigate the lines of symmetry for regular polygons.
Number of Sides
Number of Lines of
Symmetry
3
4
5
6
n
Make a general statement describing the relationship between the number of sides and
the number of lines of symmetry that can be drawn in a polygon.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
Reflecting on the Cartesian Plane
Reflect Across the x-axis
Point
A (-7,6)
B (-8,3)
C (-3, 6)
D (-2, 3)
Image
18
Reflect Across the y-axis
Point
A (-7,6)
B (-8,3)
C (-3, 6)
D (-2, 3)
Image
Practice Reflecting on the Cartesian Plane
Reflecting Across A Horizontal Line
Reflect across the horizontal line through 4
on the y-axis
Point
Image
A(
,
)
B(
,
)
C(
,
)
A’(
,
)
19
Reflecting Across A Vertical Line
Reflect across the y-axis
Point
Image
A(
,
)
B(
,
)
C(
,
)
D(
,
)
A’(
,
)
Reflecting Across An Oblique Line
Reflect across the line through (2,2) and (6,6)
P
Q
Point
R
T
Complete:
S
Pages 357-359 #’s 3, 6, 10
Symmetry and More! Sheet
Practice Book pages 295-296
Image
P(
,
)
Q(
,
)
R(
,
)
S(
,
)
T(
,
)
P’(
,
)
20
Section 7.6: Rotations and Rotational Symmetry
Rotational Symmetry
A figure has rotational symmetry if it can be turned around its center to
match itself in less than 360° turn.
The number of times in one complete turn that a figure matches itself is referred
to as: the order of rotational symmetry (triangle has an order or 3) OR the degree
of rotational symmetry (triangle has a degree of 3).
Angle of Rotation Symmetry
The minimum angle required for a shape to rotate and coincide with itself
_______360o______
The order of rotation
Polygon Summary
Number of
Sides
3
4
5
6
Degree or Order of Rotational
Symmetry
Try these
Order of Rotational Symmetry
Angle of Rotation Symmetry
Order of Rotational Symmetry
Angle of Rotation Symmetry
Angle of Rotation
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Order of Rotational Symmetry
Angle of Rotation Symmetry
What do you think the order of symmetry is for a circle?
What if you know the angle of rotation symmetry and you are asked to find the
order of rotational symmetry?
Examples:
What is the order of rotational symmetry for each angle of rotation symmetry?
A) 90o
B) 120o
You can create your own figure with rotational symmetry by rotating a shape about
a vertex.
The new shape has rotational symmetry of order _____ .
Complete:
Pages 365 – 366 #’s 4 to 8 & 12
22
Section 7.7
Identifying Types of Symmetry on the Cartesian Plane
We will be completing translations, reflections and rotations to an image to see if it has
reflectional or rotational symmetry.
Example 1:
Draw rectangle ABCD after each transformation. Write the coordinates of each new
vertex. Describe whether or not reflectional or rotational symmetry exists?
a). a rotation of 1800 about the origin
y
4
Point
A (-1,1)
B (3, 1)
C (3, 0)
D (-1, 0)
Image
2
-4
-2
2
x
4
-2
-4
y
b). a reflection along the x-axis
4
2
Point
A (-1,1)
B (3, 1)
C (3, 0)
D (-1, 0)
Image
-4
-2
2
4
-2
-4
c). a translation 3 units right and 1 units down
Point
A (-1,1)
B (3, 1)
C (3, 0)
D (-1, 0)
y
Image
4
2
-2
2
-2
-4
4
6
8
x
x