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Unit Map 2012-2013 City School District of Albany Collaboration / Geometry District Curriculum September 2012* (C) / Grade 10 (District High School Curriculum) Tuesday, January 15, 2013, 9:54AM Unit: Triangle Properties & Congruence (Week 8, 8 Weeks) Priority Standards Math (2005), HS: Geometry, Geometry Locus G.G.21 Investigate and apply the concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors of triangles Students will identify and justify geometric relationships formally and informally. Informal and Formal Proofs G.G.27 Write a proof arguing from a given hypothesis to a given conclusion G.G.28 Determine the congruence of two triangles by using one of the five congruence techniques (SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two congruent triangles G.G.29 Identify corresponding parts of congruent triangles G.G.36 Investigate, justify, and apply theorems about the sum of the measures of the interior and exterior angles of polygons G.G.37 Investigate, justify, and apply theorems about each interior and exterior angle measure of regular polygons G.G.38 Investigate, justify, and apply theorems about parallelograms involving their angles, sides, and diagonals G.G.42 Investigate, justify, and apply theorems about geometric relationships, based on the properties of the line segment joining the midpoints of two sides of the triangle G.G.43 Investigate, justify, and apply theorems about the centroid of a triangle, dividing each median into segments whose lengths are in the ratio 2:1 G.G.48 Investigate, justify, and apply the Pythagorean theorem and its converse Supporting Standards SUPPORTING: CCLS:Mathematics, HS: Geometry, Congruence G-CO Understand congruence in terms of rigid motions 8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. G-CO Prove geometric theorems 9. Prove theorems about lines and angles. 10. Prove theorems about triangles. SUPPORTING: CCLS:Mathematics, HS: Geometry, Similarity, Right Triangles, & Trigonometry G-SRT Define trigonometric ratios and solve problems involving right triangles 6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. 8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. SUPPORTING: CCLS:Mathematics, HS: Geometry, Circles G-C Understand and apply theorems about circles 3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. "Unwrapped" Content concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors of triangles theorems about: the sum of the measures of the interior and exterior angles of polygons each interior and exterior angle measure of regular polygons parallelograms involving their angles, sides, and diagonals geometric relationships, based on the properties of the line segment joining the midpoints of two sides of the triangle the centroid of a triangle, dividing each median into "Unwrapped" Skills INVESTIGATE and APPLY the concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors of triangles INVESTIGATE, JUSTIFY and APPLY theorems about angles, diagonals and sides WRITE a proof arguing from a given hypothesis to a given conclusion IDENTIFY corresponding parts DETERMINE the congruence of triangles Bloom's Taxonomy Levels 2, 4 (know and apply points of concurrency) 2, 4, 6 (investigate, apply and justify) 3 (write) 1 (identify) 3 (determine) segments whose lengths are in the ratio 2:1 the Pythagorean theorem and its converse proof arguing from a given hypothesis to a given conclusion corresponding parts of congruent triangles congruence of two triangles by using one of the five congruence techniques (SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two congruent triangles Big Ideas Essential Questions concept of proof How is it possible to prove that two figures are congruent or not congruent? concept of corresponding parts Does order matter when comparing figures? definitions of medians, altitudes, bisectors, What relationships remain the same and which change when constructing medians and bisectors? diagonals, midpoints congruence vs similar What is the difference between congruent shapes and similar shapes? Themes Vocabulary Terms & Concepts congruence corresponding parts similarity bisectors medians perpendicular proof diagonals exterior angles interior angles parallelogram centroid incenter circumcenter Standardized Assessment Informal Progress Monitoring Checks Correlations Pre-Assessment Unit 2 post test Unit 2 pre test Unit 2 post test Post-Assessments Unit1post_b.tst Engaging Learning Experiences Research-Based Effective Teaching Strategies Identifying Similarities and Differences Summarizing and Note Taking Reinforcing Effort, Providing Recognition Homework and Practice 21st Century Learning Skills Critical thinking and Problem Solving Effective Oral and Written Communication Accessing and Analyzing Information Cooperative Learning Setting Objectives, Providing Feedback Generating and Testing Hypotheses Differentiation Strategies Specifically Designed Instruction for SPED Student Intervention Strategies (Tier 1, 2, 3) proofs_levels[2].docx Strategies for English Language Learners Enrichment/Extension Pythagorean theorem and corollary if a^2 + b^2 > c^2 then then triangle is acute if a^2 + b^2 = c^2 then then triangle is right if a^2 + b^2 < c^2 then then triangle is obtuse Always remember that the third side must be between the sum and the difference of the measures of the other two sides Instructional Resources Unit 2 post review Unit 2 post test Triangles notebook Chapter 4 review Chapter 4 test Chapter 5 review Chapter 5 test Triangles proof notebook will not upload....maybe to large? Triangles proof quiz Exit tickets Interdisciplinary Connections Unit2_post_review.tst Unit2_posttestt_v2.tst Chapter 4 Review.tst Chapter 4 test.tst proofs_levels.docx Exit ticket midsegment.docx Triangles.2012.2013.notebook Chapter 5 REVIEW.tst Quiz1 2012-2013.docx congruent.triangles.2012.2013.notebook Last Updated: Monday, January 7, 2013, 8:47PM Atlas Version 7.2.6 © Rubicon International 2013. All rights reserved