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Lesson 21 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Lesson 21: Correspondence and Transformations Classwork Opening Exercise The figure to the right represents a rotation of β³ π΄π΅πΆ 80° around vertex πΆ. Name the triangle formed by the image of β³ π΄π΅πΆ. Write the rotation in function notation, and name all corresponding angles and sides. Discussion In the Opening Exercise, we explicitly showed a single rigid motion, which mapped every side and every angle of β³ π΄π΅πΆ onto β³ πΈπΉπΆ. Each corresponding pair of sides and each corresponding pair of angles was congruent. When each side and each angle on the pre-image maps onto its corresponding side or angle on the image, the two triangles are congruent. Conversely, if two triangles are congruent, then each side and angle on the pre-image is congruent to its corresponding side or angle on the image. Lesson 21: Correspondence and Transformations This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M1-TE-1.3.0-07.2015 S.115 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 21 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Example Μ Μ Μ Μ is one diagonal of the square. β³ π΄π΅πΆ is a reflection of β³ π΄π·πΆ across segment π΄πΆ. Complete π΄π΅πΆπ· is a square, and π΄πΆ the table below, identifying the missing corresponding angles and sides. A B D C Corresponding Angles β π΅π΄πΆ β β π΄π΅πΆ β β π΅πΆπ΄ β a. Are the corresponding sides and angles congruent? Justify your response. b. Is β³ π΄π΅πΆ β β³ π΄π·πΆ? Justify your response. Lesson 21: Correspondence and Transformations This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M1-TE-1.3.0-07.2015 Corresponding Sides Μ Μ Μ Μ π΄π΅ β Μ Μ Μ Μ π΅πΆ β Μ Μ Μ Μ β π΄πΆ S.116 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 21 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY Exercises Each exercise below shows a sequence of rigid motions that map a pre-image onto a final image. Identify each rigid motion in the sequence, writing the composition using function notation. Trace the congruence of each set of corresponding sides and angles through all steps in the sequence, proving that the pre-image is congruent to the final image by showing that every side and every angle in the pre-image maps onto its corresponding side and angle in the image. Finally, make a statement about the congruence of the pre-image and final image. 1. Sequence of Rigid Motions (2) Composition in Function Notation Sequence of Corresponding Sides Sequence of Corresponding Angles Triangle Congruence Statement 2. Sequence of Rigid Motions (2) Composition in Function Notation Sequence of Corresponding Sides Sequence of Corresponding Angles Triangle Congruence Statement Lesson 21: Correspondence and Transformations This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M1-TE-1.3.0-07.2015 S.117 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Lesson 21 NYS COMMON CORE MATHEMATICS CURRICULUM M1 GEOMETRY 3. Sequence of Rigid Motions (2) Composition in Function Notation Sequence of Corresponding Sides Sequence of Corresponding Angles Triangle Congruence Statement Lesson 21: Correspondence and Transformations This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M1-TE-1.3.0-07.2015 S.118 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 M1 GEOMETRY Problem Set 1. Exercise 3 mapped β³ π΄π΅πΆ onto β³ πππ in three steps. Construct a fourth step that would map β³ πππ back onto β³ π΄π΅πΆ. 2. Explain triangle congruence in terms of rigid motions. Use the terms corresponding sides and corresponding angles in your explanation. Lesson 21: Correspondence and Transformations This work is derived from Eureka Math β’ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from GEO-M1-TE-1.3.0-07.2015 S.119 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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