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GEOMETRY 2016-2017 INSTRUCTOR: Mrs. Bechtel ROOM: 208 E-MAIL: [email protected] PHONE: 815-772-4071 TEXT: Glencoe, Geometry, 2005 PREREQUSITE: Algebra 1 MATERIALS: 3-ring binder (will be used for Geometry only) 3-ring dividers (2) loose leaf paper pencils ruler-inches and centimeters protractor calculator textbook cover DESCRIPTION: Geometry uses basic assumptions, definitions, and theorems to reason deductively to new conclusions. This process is known as formal proof. Other topics covered include congruent and similar triangles, parallel lines, polygons, quadrilaterals, circles, right triangles, trigonometry, and coordinate geometry. Each chapter incorporates some review of Algebra. EVALUATION: Grades will be based on homework, notes, vocabulary checks, quizzes, projects and tests. Semester exams are worth 20% of the semester grade. Each quarter is worth 40% of the semester grade. Extra credit will be sporadic. UNIT CHRONOLOGY AND BENCHMARKS: Chapter 1: Points, Lines, Planes and Angles Students will know and be able to: Identify and model points, lines and planes Measure segments Construct and copy line segments, angles, perpendicular lines and midpoints Bisect segments and angles Calculate the distance between points and find the midpoint of a segment Measure and classify angles and identify angle relationships Identify polygons and find their perimeters Chapter 2: Reasoning and Proof Students will know and be able to: Make conjectures, determine whether a statement is true or false, and find counterexamples for statements. Use deductive reasoning to reach valid conclusions Verify algebraic and geometric conjectures using informal and formal proof Write proofs involving segment and angle theorems Chapter 3: Parallel and Perpendicular Lines Students will know and be able to: Identify angle relationships that occur with parallel lines and a transversal, and identify and prove lines parallel from given angle relationships Use slope to analyze a line and to write its equation Chapter 4: Congruent Triangles Students will know and be able to: Classify triangles Apply the Angle Sum Theorem and the Exterior Angle Theorem Identify corresponding parts of congruent triangles Test for triangle congruence using SSS, SAS, ASA, and AAS Use properties of isosceles and equilateral triangles Write coordinate proofs Chapter 5: Relationships in Triangles Students will know and be able to: Identify and use perpendicular bisectors, angle bisectors, medians, and altitudes of triangles Apply properties of inequalities relating to the measures of angles and sides of triangles Use indirect proof with algebra and geometry Apply the Triangle Inequality Theorem and SAS and SSS inequalities Chapter 6: Proportions and Similarity Students will know and be able to: Identify similar polygons and use ratios and proportions to solve problems Recognize and use proportional parts to solve problems FALL SEMESTER EXAM Chapter 7: Right Triangles and Trigonometry Students will know and be able to: Solve problems using the Pythagorean Theorem, and its converse Use trigonometric ratios to solve right triangle problems Use the Law of Sines to solve non-right triangles Chapter 8: Quadrilaterals Students will know and be able to: Investigate interior and exterior angles of polygons Recognize and apply the properties of parallelograms Recognize and apply the properties of rectangles, rhombi, squares, and trapezoids Position quadrilaterals for use in coordinate proof Chapter 10: Circles Students will know and be able to: Identify parts of a circle and solve problems involving circumference Find arc and angle measures in a circle Find measures of segments in a circle Write the equation of a circle Chapter 11: Areas of Polygons and Circles Students will know and be able to: Find the areas of parallelograms, triangles, rhombi, trapezoids, regular polygons, and circles Find areas of irregular figures Find geometric probability and areas of sectors and segments of circles Chapter 9: Transformations Students will know and be able to: Recognize and draw reflections Recognize and draw translations Recognize and draw rotations Recognize and draw dilations Find magnitudes and directions for vectors Perform translations with vectors Add, subtract and multiply matrices Use matrices to determine the coordinates of translations, dilations, reflections and rotations Chapter 12: Surface Area Students will be able to find the surface area of: Prisms Cylinders Pyramids Cones Spheres FINAL EXAM