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INFORMAL GEOMETRY – UNIT 4 Triangles – Part I Glencoe: Geometry: Concepts and Applications Target Time Frame: 12 days ESSENTIAL STANDARD 1 – Solves problems and practical applications using appropriate approaches and tools (including calculators and computers) and judges the reasonableness of results. 2 – Uses algebraic skills and concepts to solve geometric problems throughout geometry. 3 – Uses visualization skills to explore and interpret both two- and three-dimensional geometric figures using such topics as projections, cross sections, and locus problems. 11 – Classifies triangles as acute, right, obtuse, equilateral, isosceles, scalene; and classifies polygons as regular, convex, congruent. 14 – States and applies the triangle sum, exterior angles, and polygon angle sum theorems. 15 – Identifies congruent figures and recognizes congruence in practical applications. 17 – Identifies congruent triangles and right triangles using basic congruence postulates and theorems. ESSENTIAL QUESTION How do we solve problems and practical applications and judge the reasonableness of the results? What algebra skills and concepts are used in geometry? How can visualization skills help you explore both solid and plane geometry? DEPTH for MASTERY All Throughout unit All Throughout unit All Throughout unit How do you classify a triangle? Classify triangles 5.1 What is the sume of the interior angles of a triangle? How do you prove triangles congruent? Triangle sum and exterior angles All 5.2 How do you prove right triangles congruent? All 5.5 – 5.6 6.5 Sections 5.4 – 5.6 COMMENTS ESSENTIAL STANDARD 22 – Identifies similar figures in practical applications; identifies similar triangles and other similar polygons by using their properties. 23 – Recognizes and applies properties of similar polygons using ratio and proportion. ESSENTIAL QUESTION How do you prove triangles similar? DEPTH for MASTERY Traingles How do properties relate to polygons? All ESSENTIAL QUESTION 4 – Uses inductive and deductive reasoning What is the difference to reach conclusions, identifies conjectures between inductive and deductive reasoning? and counterexamples, and describes the nature of a deductive mathematical system. 6 – Uses formal and/or informal logical How do you use formal and informal reasoning reasoning processes. processes? 13 – Applies basic facts about points, lines What are the and planes, and about perpendicular and relationships between parallel lines and planes. parallel lines inside triangles? 20 – Recognizes and applies the properties How do inequalities of inequalities to the measures of segments relate to triangles? and angles in triangles. How do properties relate 24 – Applies properties dealing with to parallel lines and parallel lines and proportion. proportion? 25 – Solves problems involving similar How do properties relate to polygons? polygons. 43 – Uses transformations to examine How do you prove triangles congruent? symmetry, similarity, and congruence of geometric figures. IMPORTANT STANDARD Sections COMMENTS 9.2 – 9.3 9.2 9.4 9.6 DEPTH for MASTERY All Throughout unit All Throughout unit Points, lines, perpendicular, and parallel lines All 9.5 All 9.3 9.6 All 9.2 All 5.4 Sections 7.3 COMMENTS COMPACT STANDARD 16 – Uses tools such as compass and straightedge, paper folding, tracing paper, mira, or computer to construct congruent segments, angles, triangles, and circles; an angle bisector; a perpendicular bisector; a perpendicular line from a point on a line; parallel lines; proportional segments; tangents; and inscribed and circumscribed polygons. EOCT Domains Taught in this Unit: UNIT COMMENTS: ESSENTIAL QUESTION How do you determine that triangles are congruent? DEPTH for MASTERY Congruent triangles, proportional segments Sections 5.5 9.4 COMMENTS