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Standard #: MAFS.912.G-CO.2.7 This document was generated on CPALMS - www.cpalms.org Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. Subject Area: Mathematics Grade: 912 Domain: Geometry: Congruence Cluster: Understand congruence in terms of rigid motions - Geometry - Major Cluster Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters. Date Adopted or Revised: 02/14 Content Complexity Rating: Level 1: Recall - More Information Date of Last Rating: 02/14 Status: State Board Approved Related Courses Course Number 1206300: 7912060: 1206315: 1206310: 1206320: Course Title Informal Geometry (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) Access Informal Geometry (Specifically in versions: 2014 2015 (course terminated)) Geometry for Credit Recovery (Specifically in versions: 2014 2015, 2015 and beyond (current)) Geometry (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) Geometry Honors (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) 7912065: 1200400: Access Geometry (Specifically in versions: 2015 and beyond (current)) Intensive Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current)) Related Access Points Access Point Access Point Number MAFS.912.G-CO.2.AP.7a Access Point Title Use definitions to demonstrate congruency and similarity in figures. Related Resources Lesson Plan Name Description This lesson is intended to help you assess how well students are able to: Analyzing Congruence Proofs Work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles. Identify and understand the significance of a counterexample. Prove, and evaluate proofs in a geometric context. This is an exploratory lesson that elicits the relationship Exploring Congruence Using between the corresponding sides and corresponding angles of Transformations two congruent triangles. Students will prove that two figures are congruent based on a rigid motion(s) and then identify the corresponding parts using Match That! paragraph proof and vice versa, prove that two figures are congruent based on corresponding parts and then identify which rigid motion(s) map the images. Slip, Slide, Tip, and Turn: Using the definition of congruence in terms of rigid motion, Corresponding Angles and students will show that two triangles are congruent. Corresponding Sides Formative Assessment Name Description Students are given two congruent triangles and asked to Congruence Implies determine the corresponding side lengths and angle measures Congruent Corresponding and to use the definition of congruence in terms of rigid motion Parts to justify their reasoning. Proving Congruence Using Students are asked to prove two triangles congruent given that Corresponding Parts all pairs of corresponding sides and angles are congruent. Students are given two triangles in which all pairs of Showing Congruence Using corresponding parts are congruent and are asked to use the Corresponding Parts - 1 definition of congruence in terms of rigid motion to show the triangles are congruent. Students are given two triangles in which all pairs of Showing Congruence Using corresponding parts are congruent and are asked to use the Corresponding Parts - 2 definition of congruence in terms of rigid motion to show the triangles are congruent. Students are asked to use the definition of congruence in terms Showing Triangles Congruent of rigid motion to show that two triangles are congruent in the Using Rigid Motion coordinate plane. Virtual Manipulative Name Congruent Triangles Description This manipulative is a virtual realization of the kind of physical experience that might be available to students given three pieces of straws and told to make them into a triangle. when working with pieces that determine unique triangles (SSS, SAS, ASA). Students construct triangles with the parts provided. After building a red and a blue triangle, students can experience congruence by actually moving one on the top of the other. Problem-Solving Task Name Reflections and Equilateral Triangles II Description This task gives students a chance to see the impact of reflections on an explicit object and to see that the reflections do not always commute. Assessment Name Sample 1 - High School Geometry State Interim Assessment Description This is a State Interim Assessment for 9th-12th grade. Sample 2 - High School Geometry State Interim Assessment Sample 3 - High School Geometry State Interim Assessment Sample 4 - High School Geometry State Interim Assessment This is a State Interim Assessment for 9th-12th grade. This is a State Interim Assessment for 9th-12th grade. This is a State Interim Assessment for 9th-12th grades. Student Resources Name Congruent Triangles Reflections and Equilateral Triangles II Description This manipulative is a virtual realization of the kind of physical experience that might be available to students given three pieces of straws and told to make them into a triangle. when working with pieces that determine unique triangles (SSS, SAS, ASA). Students construct triangles with the parts provided. After building a red and a blue triangle, students can experience congruence by actually moving one on the top of the other. This task gives students a chance to see the impact of reflections on an explicit object and to see that the reflections do not always commute. Parent Resources Name Congruent Triangles Reflections and Equilateral Triangles II Description This manipulative is a virtual realization of the kind of physical experience that might be available to students given three pieces of straws and told to make them into a triangle. when working with pieces that determine unique triangles (SSS, SAS, ASA). Students construct triangles with the parts provided. After building a red and a blue triangle, students can experience congruence by actually moving one on the top of the other. This task gives students a chance to see the impact of reflections on an explicit object and to see that the reflections do not always commute.