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INFORMAL GEOMETRY – UNIT 7 Polygons and Circles – Part II Glencoe: Geometry: Concepts and Applications Target Time Frame: 11 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. 26 – States and applies the Pythagorean Theorem and its converse. 27 – States and applies properties of special right triangles, such as 45-45-90 and 30-60-90 triangles. 28 – Identifies and evaluates tangent, sine, and cosine ratios for an acute angle of a right triangle; uses a table, calculator, or computer to find the ratio for a given angle or find the angle for a given ratio. 29 – Uses the tangent, since, and cosine ratios for right triangles to solve application problems such as indirectmeasurement problems. 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 What is the Pythagorean Theorem and how is it used? What are the properties of special right triangles? How are they used? All 6.6 All 13.2 – 13.3 What is SohCahToa and how is it used to solve problems? All 13.4 What is SohCahToa and how is it used to solve problems? All 13.4 Sections COMMENTS Supplement – Teach simplifying square roots without calculators ESSENTIAL QUESTION 30 – Identifies and defines circles and their What are the parts of a circle? How do we parts (center, arc, interior, exterior); identify different types of segments and lines associated with circles (chord, diameter, radius, tangent, secant); arcs? properties of circles (congruent, concentric, tangent); relationship of polygons and circles (inscribed, circumscribed); angles (central; inscribed; formed by tangents, chords, and secant). 31 – Applies geometric relationships to How do you find the measure of different arcs, solving problems, such as relationships angles, and segments? between lines and segments associated with circles, the angles they form, and the arcs they subtend; and the measures of these arcs, angles, and segments. 34 – Finds the area of triangles, What is the formula for parallelograms, rectangles, squares, finding the area of a trapezoids, regular polygons, circles, and sector and how do you apply it? sectors. ESSENTIAL STANDARD DEPTH for MASTERY Parts of a circle, arcs 11.1 – 11.4 All 11.1, 11.2, 11.3 Area of sector 11.6 Sections COMMENTS Area of sector only 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? IMPORTANT STANDARD EOCT Domains Taught in this Unit: UNIT COMMENTS: DEPTH for MASTERY All Throughout unit All Throughout unit Sections COMMENTS