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### Chapter 4--Discovering and Proving Triangle Properties

 Essential Question:  How can we use inductive and deductive geometric reasoning to make and prove the conjectures about triangles? Unit Rationale:  Developing valid inductive and deductive arguments, using our familiarity with triangles, builds the foundation for general strategic thinking within and outside the world of mathematics. As a result of this unit, students will be able to prove and apply properties of triangles listed below using paragraphs, flowcharts, and two-column formats: 1.       The Triangle Sum Conjecture 2.       Isosceles Triangle Conjecture and its Converse 3.       Triangle Inequality Conjecture 4.       Side-Angle Inequality Conjecture 5.       Triangle Exterior Angle Conjecture 6.       Shortcuts to Triangle Congruence 7.       CPCTC   Vocabulary: ·         Isosceles triangle properties ·         Equilateral triangle properties ·         Interior and Exterior Angles ·         Congruent/Congruence ·         Triangle Congruence shortcuts (SSS, SAS, ASA, AAS) ·         Corresponding Parts of Congruent Triangles are Congruent (CPCTC) ·         Midpoint/Bisect/Angle Bisector Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements.  Focus Standards: *G.1.F Distinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems. G.2.D Describe the intersections of lines in the plane and in space, of lines and planes, and of planes in space. Supporting Standards: G.3.K Analyze cross-sections of cubes, prisms, pyramids, and spheres and identify the resulting shapes. *G.4.B Determine the coordinates of a point that is described geometrically. *G.1.E Identify errors or gaps in a mathematical argument and develop counterexamples to refute invalid statements about geometric relationships. Reasoning, Problem Solving, and Communication Standards: *G.7.A Analyze a problem situation and represent it mathematically. *G.7.B Select and apply strategies to solve problems. G.7.E Read and interpret diagrams, graphs, and texts containing the symbols, language and conventions of mathematics.