Unit 6: Scale Factor and Unit 6: Scale Factor and MeasurementMeasurement

How will you measure up?How will you measure up?

Similar figuresSimilar figuresWhat am I Learning Today?What am I Learning Today?

How will I show that I learned it?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

VocabularyVocabulary Corresponding: The relationship Corresponding: The relationship

between the sides and angles of two between the sides and angles of two or more objects that are matchedor more objects that are matched

Similar: Figures with the same shape, Similar: Figures with the same shape, but not necessarily the same sizebut not necessarily the same size

Congruent: Figures that have the Congruent: Figures that have the same size and shapesame 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 aboutWhat do you remember aboutRatio and Proportion?Ratio and Proportion?

See if you can answer these…See if you can answer these…

1) What is a ratio? 1) What is a ratio?

A comparison of two quantities measured in A comparison of two quantities measured in the same unitsthe same units

2) What is a proportion?2) What is a proportion?

An equation that shows two ratios are An equation that shows two ratios are equivalentequivalent

3) Explain how you find a missing value in a 3) Explain how you find a missing value in a proportion.proportion.

Find the cross products. Isolate the variable Find the cross products. Isolate the variable using the inverse operation.using the inverse operation.

Questions AnswersQuestions Answers

How do I know two figures are

similar?

What is a tic-tac-toe grid?

1) The measure of the corresponding angles are equal2) 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 sides2) Use a tic-tac-toe grid to help set up the proportion correctly.3) Solve proportion using cross product.

L1 L2

W1W2

= orL1 W1

L2W2

=

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.

Similar Figures

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.

3

5

4

915

12

333

3

8

6

52 y

___ 50 100

____ = Write a proportion using corresponding side lengths.

The cross products are equal.100 • 52 = 50 • y

A B60 m 120 m

50 m 100 m

y52 m

The two triangles are similar. Find the missing length y.

y is multiplied by 50.5,200 = 50yDivide both sides by 50 to undo the multiplication.

5,200 50

_____ 50y 50

___ =

y =104 meters

54 • 3 = 2 • w

162 = 2w

162 2

____ 2w 2

___ =

81 = w

The width of the actual painting is 81 cm.

Write a proportion.

The cross products are equal.

w is multiplied by 2.

Divide both sides by 2 to undo the multiplication.

3 cm w cm

2 cm 54 cm

_____ =

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?

Let’s PracticeLet’s Practice

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