Unit 6: Scale Factor and
Measurement
How will you measure up?
What am I Learning Today?
Similar figures
How will I show that I learned it?
Demonstrate the relationship between similar
plane figures using ratio and proportion
Use proportions to find missing measures in
similar figures
Solve problems using proportions
Vocabulary


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Corresponding: The relationship between
the sides and angles of two or more
objects that are matched
Similar: Figures with the same shape, but
not necessarily the same size
Congruent: Figures that have the same
size and shape
Matching sides of two or more polygons are called
corresponding sides, and matching angles are called
corresponding angles.
What do you remember about
Ratio and Proportion?
See if you can answer these…
1) What is a ratio?
A comparison of two quantities measured in the
same units
2) What is a proportion?
An equation that shows two ratios are equivalent
3) Explain how you find a missing value in a
proportion.
Find the cross products. Isolate the variable using
the inverse operation.
Questions
Answers
How do I know
two figures are
similar?
1) The measure of the corresponding angles are
equal
2) The ratios of the lengths of the corresponding
sides are proportionate
How can I find
the length of a
missing side of
similar figures?
1) Write a proportion using corresponding sides
2) Use a tic-tac-toe grid to help set up the
proportion correctly.
3) Solve proportion using cross product.
What is a tictac-toe grid?
L1
L2
W1
=
W2
or
L1
L2
=
W1
W2
For example, ratios should be set up to compare length to
length and width to width, which puts the first shape as
both numerators and the second as both denominators.
OR Ratios should compare a shape’s length to its width,
which gives each shape its own ratio.
Figures that have the same
shape, but may not be the
same size. They also do not
have to be in the
same position.
• Matching sides are
proportional
• Matching angles have the
same measure.
Similar
Figures
5
3
4
9
6
8
15
3
3
12
3
3
The two triangles are similar. Find the
missing length y.
A
60 m
50 m
B
120 m
100 m
52 m
y
50 = ___
52
Write a proportion using
____
corresponding side lengths.
100
y
100 • 52 = 50 • y The cross products are equal.
y is multiplied by 50.
5,200 = 50y
5,200 =
_____
50
y =104
50y
___
50
meters
Divide both sides by 50 to
undo the multiplication.
This reduction is similar to a picture
that Katie painted. The height of the
actual painting is 54 centimeters.
What is the width of the actual
painting?
2 cm
3 cm
_____
=
w cm Write a proportion.
54 cm
54 • 3 = 2 • w The cross products are equal.
162 = 2w
162
2w
____
___
=
2
2
w is multiplied by 2.
Divide both sides by 2 to
undo the multiplication.
81 = w
The width of the actual painting is 81 cm.
Let’s Practice
http://www.harcourtschool.com/activity/similar_congruent/
http://www.quia.com/rr/232263.html?AP_rand=243379547