Unit 6 Lesson 6.3: Corresponding Parts of Similar Figures

​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.

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. ​

​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 . . . ​

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

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Conclusion: ABCD ∼ JKLM

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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Angles: CONGRUENT

Sides: PROPORTIONAL​