Similar Figures Study Guide

Similar Figures Study Guide

Remember to take notes inside of your notebook. Ask Mrs. Miller if you have any questions.

types of similar figures

1) Identifying similar figures

2) Calculating scale factor

3) Finding a missing measurement​

Subject | Subject

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identifying similar figures

Remember that similar figures must have two qualities:

1) Their angles must be congruent (equal or the same)

2) Their sides must be proportional (shrinking or growing by the same amount)​

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1) Identify the corresponding sides (longest with longest, shortest with shortest)

2)​ Set up a proportion (Butterfly ratios)

3) ​Cross multiply the wings.

4) If the wings are equal, the figures are similar.​

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In this example, the wings are not equal, so these figures are not similar.​

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To determine if two figures are similar:

Multiple Choice

Are the following similar? Why or why not?

• Yes
• No, the corresponding angles are not equal.
• No, the ratios of the corresponding sides are not equal.

Multiple Choice

Tell whether the two figures are similar. Explain your reasoning. (Hint: are they proportional?)

• Yes, similar because they are the same shape and side lengths are proportional.
• No, not similar because they are the same shape, but side lengths are not proportional.
• Yes, same shape
• No, different sizes

Multiple Choice

Are these triangles similar?

• Yes
• No

Multiple Choice

A rectangle has dimensions 4 ft. by 3 ft. Which of the following could be a rectangle that is similar?

• 8 ft. by 9 ft.

• 20 ft. by 15 ft.

• 7 ft. by 6 ft.

• 16 ft. by 15 ft.

Multiple Choice

The diagram shows a rectangle that is 4 in by 7 in in measure.

Which is the measure of a rectangle that is similar to the rectangle above?

• 4 in x 17 in

• 24 in x 42 in

• 7 in x 10 in

• 5 in x 8 in

calculating scale factor

Scale factor is the ratio by which the sides of a figure are increased or decreased. Scale factors are multiplied by.

Scale factor is written as

model : actual or model/actual (model divided by actual)​

It can also be written as

new : original or new/original ​

Let's look at some examples​.

(SIMPLIFY YOUR SCALE FACTORS)

In the first example, the new triangle has a size of 2 units and the original has a size of 1 unit. The scale factor is 2:1.

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In the second example, the new triangle has a size of 1 unit and the original has a size of 2 units. The scale fact is 1/2.

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here are two examples

Another example:

The scale of model:actual for the model cars that jeff is creating is 1:5. What does this mean?

This means that when the model is 1 unit, the actual car is 5 units.​

Multiple Choice

What is the formula for scale factor?

• $$\frac{new}{old}$$

• $$\frac{old}{new}$$

Multiple Choice

The formula for scale factor is:

• actual:model

• model: actual

• neither

• both

Multiple Choice

What is the scale factor from the large triangle to the small triangle?

• 1/2
• 2/3
• 3/4
• 2

To do this, create a proportion.

Cross multiply and solve for the variable.​

In this example, we can set up a proportion of inches over miles. Then, we cross multiply and find out there are 1, 320 miles between the two countries.

You can use scale factor to find missing measurements.

Multiple Choice

Scale is 1cm = 8km. Hatboro and Smithville are 24cm apart on the map, what is the actual distance between the 2 cities?

• 87 km
• 216 km 
• 33 km
• 192 km

Multiple Choice

On a map, Memphis, Tennessee, and Jackson, Mississippi, are 5 inches apart. The distance between the cities is actually 210 miles.

What scale was used to create the map?

• 42 inches = 1 mile
• 1 inch = 42 miles
• 40 inches = 1 mile
• 
  1 inch = 40 miles

Multiple Choice

Robbie made a scale drawing of a neighborhood park. A soccer field in the park is 14 inches long in the drawing. The actual field is 98 yards long. What is the scale of the drawing?1 inch = _ yards

• 1372
• 5
• 14
• 7

Finding the missing measurement:

To find missing measurements:

1) Identify the corresponding sides (longest with longest, shortest with shortest)

2) SET UP A PROPORTION (butterfly method)

3) Cross multiply and solve for missing measurement ​

In the example, the butterfly method was used to find the missing side.

In rectangle A, the long side over the short side = 6/4. In rectangle B, the long side over short side = x/10. The same side should be at the same spot in each proportion.

Example:

If you see a problem that combines more than one triangle into one shape, redraw the triangles as two separate triangles.

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Then, use the butterfly method to find the missing side.​

Combined triangles

If you see a problem that combines more than one triangle into one shape, redraw the triangles as two separate triangles.

Then, use the butterfly method to find the missing side.​

For the bigger triangle, be sure to add the two numbers on the long side.​

Combined triangles

Multiple Choice

Matching sides are called

• Corresponding Sides
• Corresponding Angles
• The Same
• Congruent Sides

Multiple Choice

The two right triangles below are similar. What is x, the missing side length in triangle DEF? 

• 3.75
• 9.75
• 10
• 12

Multiple Choice

The pair of figures is similar. Find the missing side.

• x = 10
• x = 4
• x = 2
• x = 5

Multiple Choice

Solve the proportion.
____ = ____

• p=31.3
• p=308
• p=924
• p=532

Multiple Choice

What is the measure of x?

• 12
• 15
• 6
• 9

Multiple Choice

Line CB corresponds with what line? 

• SR
• PQ
• SP
• RQ

Multiple Choice

Which side length on the scaled copy corresponds to the side length HJ on the original image?

• AB

• BC

• AC

Multiple Choice

Which proportion is true?

• $$\frac{6}{2.5}=\frac{x}{21}$$

• $$\frac{6}{2.5}=\frac{21}{x}$$

• $$\frac{6}{21}=\frac{x}{2.5}$$

• $$\frac{6}{x}=\frac{2.5}{21}$$