Unit 6 Lesson 6.3: Corresponding Parts of Similar Figures

Unit 6 Lesson 6.3: Corresponding Parts of Similar Figures

MT: Using Transformations to Prove Similarity

Proficiency Scale:

​Corresponding Parts of Similar Figures are Similar

​Remember CPCTC? (Corresponding Parts of Congrunet Figures are Congruent)

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We're looking at the same ​thing here, except now the figures won't always be the same size.

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Remember that CORRESPONDING means that an element from the pre-image is in the same position/spot​ as an element from the image.

Vocabulary

Multiple Choice

RECALL:

Which is the correct formula for calculating a scale factor?

• $$r=\frac{image}{pre-image}$$  

• $$k=\frac{big\ side}{small\ side}$$  

• $$r=\frac{pre-image}{image}$$  

• $$k=\frac{small\ side}{big\ side}$$  

Multiple Choice

POP QUIZ!

If two figures are similar, corresponding angles will be . . .

• supplementary

• dilated

• congruent

Multiple Choice

POP QUIZ . . . AGAIN!

If two figures are similar, then all scale factors must be . . .

• less than 1

• equal

• greater than 1

Review: Verifying Similarity Using Properties

Consider the graph of ABCD and JKLM, where ABCD is the pre-image (blue) and JKLM is the image (red). Determine if the given figures are similar.

• Remember from Lesson 6.1: Check that these properties have been satisfied:

• • ​All angles measures are congruent.

  • All scale factors are equal. ​

Review: Comparing Angles and Scale Factors

​Since all pairs of corresponding angles are congruent, this property has been satisfied.

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Now we need to check the scale factors . . . ​

Review: Comparing Angles and Scale Factors

​Since all ratios equal the same scale factor, this property has been satisfied.

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Conclusion: ABCD ∼ JKLM

Making a Conclusion:

If both properties are satisfied, you can conclude that the two figures you observed are similar.

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When they are similar, the conclusion statement will look like this:

" ΔABC ∼ ΔDEF "​

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If at least one piece of information from either property is not met, then the figures cannot be similar. ​

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Multiple Choice

Determine if the following two figures are similar by verifying (1) angle measures are preserved and (2) all scale factors are equal.

• NO

• YES

Multiple Choice

Which scale factor was used to prove that ABCD (pre-image) is similar to JKLM (image)?

• $$90\degree$$  

• 2

• 0.5

Multiple Choice

Determine if the following two figures are similar by verifying (1) angle measures are preserved and (2) all scale factors are equal.

• NO

• YES

Properties of Similar Figures

Angles: CONGRUENT

Sides: PROPORTIONAL​

Writing Proportions

Writing Proportions Practice:

Multiple Choice

Which similarity statement CAN be used to determine if the two figures are similar?

• $$\angle A\cong\angle X$$  

• $$\angle Y\cong\angle C$$  

• $$\angle B\cong\angle Z$$  

• $$\angle W\cong\angle D$$  

Multiple Choice

Which similarity statement CAN be used to determine if the two figures are similar?

•   $$\frac{AD}{WZ}=\frac{AB}{XY}$$  

• $$\frac{ZW}{AD}=\frac{YX}{BC}$$   

•   $$\frac{XY}{BC}=\frac{YZ}{CD}$$  

•   $$\frac{CD}{XY}=\frac{BC}{YZ}$$  

Multiple Choice

Which similarity statement CANNOT be used to determine if the two figures are similar?

• $$\frac{AB}{QR}=\frac{BC}{RS}$$  

• $$\angle T\cong\angle D$$  

• $$\angle A\cong\angle Q$$  

• $$\frac{DC}{ST}=\frac{BC}{SR}$$