Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM 8•3 Lesson 8: Similarity Classwork Example 1 1 2 In the picture below we have a triangle π΄π΅πΆ, that has been dilated from center π, by a scale factor of π = . It is noted by π΄′π΅′πΆ′. We also have triangle π΄′′π΅′′πΆ′′, which is congruent to triangle π΄′π΅′πΆ′ (i.e., βπ΄′π΅′πΆ′ ≅ βπ΄′′π΅′′πΆ′′). Describe the sequence that would map triangle π΄′′π΅′′πΆ′′ onto triangle π΄π΅πΆ. Lesson 8: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Similarity 2/9/16 S.32 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 32 Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM 8•3 Exercises 1. 1 2 Triangle π΄π΅πΆ was dilated from center π by scale factor π = . The dilated triangle is noted by π΄′π΅′πΆ′. Another triangle π΄′′π΅′′πΆ′′ is congruent to triangle π΄′π΅′πΆ′ ( i.e., βπ΄′′π΅′′πΆ′′ ≅ βπ΄′π΅′πΆ′). Describe the dilation followed by the basic rigid motion that would map triangle π΄′′π΅′′πΆ′′ onto triangle π΄π΅πΆ. Lesson 8: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Similarity 2/9/16 S.33 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 33 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 8 8•3 2. Describe the sequence that would show βπ΄π΅πΆ~βπ΄′ π΅′ πΆ ′ . 3. Are the two triangles shown below similar? If so, describe the sequence that would prove βπ΄π΅πΆ~βπ΄′π΅′πΆ′. If not, state how you know they are not similar. Lesson 8: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Similarity 2/9/16 S.34 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 34 NYS COMMON CORE MATHEMATICS CURRICULUM 4. Lesson 8 8•3 Are the two triangles shown below similar? If so, describe the sequence that would prove βπ΄π΅πΆ~βπ΄′π΅′πΆ′. If not, state how you know they are not similar. Lesson 8: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Similarity 2/9/16 S.35 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 35 Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM 8•3 Lesson Summary Similarity is defined as mapping one figure onto another as a sequence of a dilation followed by a congruence (a sequence of rigid motions). The notation, βπ΄π΅πΆ~βπ΄′ π΅′ πΆ ′ , means that βπ΄π΅πΆ is similar to βπ΄′π΅′πΆ′. Problem Set 1. In the picture below, we have a triangle π·πΈπΉ, that has been dilated from center π, by scale factor π = 4. It is noted by π·′πΈ′πΉ′. We also have a triangle π·′′πΈ′′πΉ′′, which is congruent to triangle π·′πΈ′πΉ′ (i.e., βπ·′πΈ′πΉ′ ≅ βπ·′′πΈ′′πΉ′′). Describe the sequence of a dilation, followed by a congruence (a sequence of one or more rigid motions), that would map triangle π·′′πΈ′′πΉ′′ onto triangle π·πΈπΉ. Lesson 8: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Similarity 2/9/16 S.36 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 36 Lesson 8 NYS COMMON CORE MATHEMATICS CURRICULUM 2. 8•3 1 2 Triangle π΄π΅πΆ was dilated from center π by scale factor π = . The dilated triangle is noted by π΄′π΅′πΆ′. Another triangle π΄′′π΅′′πΆ′′ is congruent to triangle π΄′π΅′πΆ′ (i.e., βπ΄′′π΅′′πΆ′′ ≅ βπ΄′π΅′πΆ′). Describe the dilation followed by the basic rigid motion that would map triangle π΄′′π΅′′πΆ′′ onto triangle π΄π΅πΆ. 3. Are the two figures shown below similar? If so, describe the sequence that would prove the similarity. If not, state how you know they are not similar. Lesson 8: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Similarity 2/9/16 S.37 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 37 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 8 8•3 4. Triangle π΄π΅πΆ is similar to triangle π΄′π΅′πΆ′, (i.e, βπ΄π΅πΆ~βπ΄′π΅′πΆ′). Prove the similarity by describing the sequence that would map triangle π΄′π΅′πΆ′ onto triangle π΄π΅πΆ. 5. Are the two figures shown below similar? If so, describe the sequence that would prove βπ΄π΅πΆ~βπ΄′π΅′πΆ′. If not, state how you know they are not similar. 6. Describe the sequence that would show βπ΄π΅πΆ~βπ΄′ π΅′ πΆ ′ . Lesson 8: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Similarity 2/9/16 S.38 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 38