Similarity Statements and Scale Factors

​Similarity

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​Some text here about the topic of discussion.

Take a look at these 2 triangles

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Open Ended

Which side corresponds to side CB?

SCALE FACTOR

Scale factor: The amount each side of a figure is multiplied by when the figure is proportionally enlarged or reduced in size.

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Open Ended

What is the scale factor from the small "C" to the big "C"?

Proportion

An equation of two equivalent fractions

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You can solve them by cross multiplying. ​

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Multiple Choice

Which equation would be the correct proportion to set up?

• $$\frac{8}{x}=\frac{72}{6}$$  

• $$\frac{x}{6}=\frac{72}{8}$$  

• $$\frac{x}{8}=\frac{72}{6}$$  

• $$\frac{6}{72}=\frac{x}{8}$$  

Open Ended

Solve the proportion for this problem. Use cross multiplication. Write your answer as x=#

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Rochida drew ΔABC below and then dilated through point A to create ΔAB′C′.

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These two triangles are difficult to compare, so Rochida redrew them separately.​

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Draw

Write a proportion (fraction = fraction)

Similarity Conditions

​Angle Angle

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Side-Angle-Side​

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Side-Side-Side​

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If you have 2 angles that are the same, triangles are similar.

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If you have 2 sides that are proportional and the angle between them is congruent, triangles are similar.​

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If you have 3 sides that are proportional, triangles are similar.​

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Multiple Choice

What is the similarity statement for the triangle pair?

• ΔXYZ is similar to ΔNEW

• ΔXZY is similar to ΔNWE

• ΔZYX is similar to ΔENW

• ΔYZX is similar to ΔNWE

Multiple Choice

Is Triangle ABC similar to Triangle DEF?

• Yes, by SSS

• Yes, by SAS

• No, because the corresponding sides are not proportional.

• No, because we don't know if the included angles are congruent.

Multiple Choice

Determine if Triangle VEZ is similar to Triangle MAG

• No, because all of the angles are congruent.

• Yes, by AA

• No, because the sides are not proportional.

• Yes, by SAS

Multiple Choice

State if the triangles in each pair are similar. If so, state how you know they are similar.

• Yes, AA Similarity

• Yes, SSS Similarity

• Yes, SAS Similarity

• Not Similar

Multiple Choice

State if the triangles in each pair are similar. If so, state how you know they are similar.

• Yes, AA Similarity

• Yes, SSS Similarity

• Yes, SAS Similarity

• Not Similar