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1 Basic Course Information Title: A-G Geometry Transcript abbreviations: Geo A / Geo B Length of course: Full Year Subject area: Mathematics ("c") / Geometry UC honors designation? No Prerequisites: None Co-requisites: None Integrated (Academics / CTE)? No Grade levels: 9th, 10th Course learning environment: Classroom Based Course Description Course overview: Course Purpose This Geometry course emphasizes the study of the basic elements of geometry, proofs, parallel and perpendicular lines, congruence and relationships in triangles and quadrilaterals, proportions and similarity, right triangles and trigonometry, transformations and symmetry, measurements of circles, surface area and volume, and probability and measurement. This is a one-year Geometry course that provides a comprehensive look at the study of geometric concepts.â Students are challenged to develop critical thinking and creative problem solving skills to meet the Common Core Standards in Geometry and learn geometric concepts including: the basic elements of geometry, proofs, parallel and perpendicular lines, congruence and relationships in triangles and quadrilaterals, proportions and similarity, right triangles and trigonometry, transformations and symmetry, measurements of circles, surface area and volume, and probability and measurement. This course was written around the 2015 Houghton Mifflin Harcourt Common Core edition of Geometry textbook, but was specifically written to align with any Common Core textbook for Geometry or similar resource.
2 Course content: Course Objectives Course Objectives: Identify and model points, lines, and planes and intersecting lines and planes Measure segments and calculate with measures Find the distance between two points and midpoint of a segment Measure, classify, and identify and use congruent angles, and the bisector of an angle Identify and use special pairs of angles and perpendicular lines Identify and name polygons Find perimeter, circumference, and area of two-dimensional figures Identify and name three-dimensional figures and find surface area and volume Make conjectures based on inductive reasoning and find counterexamples Determine truth values of negations, conjectures, and disjunctions and represent them using Venn Diagrams Analyze statements in if-then form and write converses, inverses, and contrapositives Use the Law of Detachment and the Law of Syllogism Identify and use basic postulates about points, lines, and planes, and write paragraph proofs Use algebra to write two-column proofs and use properties of equality to write geometric proofs Write proofs involving segment addition and involving congruence Write proofs involving supplementary and complementary angles, congruent, and right angles Identify the relationship between two lines or two planes and name pairs formed by parallel lines and transversals Use theorems to determine the relationships between specific pairs of angles and use algebra to find angle measurements Find slopes of lines and use slope to identify parallel and perpendicular lines Write an equation of a line given information about the graph and solve problems by writing equations Recognize angle pairs that occur with parallel lines and prove that two lines are parallel Find the distance between a point and a line and between two parallel lines Identify and classify triangles by angle measures and side measures Apply the Triangle Angle-Sum Theorem and the Exterior Angle Theorem Name and use corresponding parts of congruent polygons and prove triangles congruent using the definition of congruence Use the SSS and SAS postulates to test for triangle congruence Use the ASA and AAS Postulates to test for triangle congruence Use properties of isosceles and equilateral triangles Identify reflections, translations, and rotations and verify congruence after a congruence transformation Position and label triangles for use in coordinate proofs and write coordinate proofs Identify and use perpendicular bisectors in triangles and use angle bisectors in triangles Identify and use medians in triangles and altitudes in triangles
3 Recognize and apply properties of inequalities to the measures of the angles of a triangle and to the relationships between the angles and the sides of a triangle Write indirect algebraic proofs and indirect geometric proofs Find and use the sum of the measures of the interior and exterior angles of a polygon Recognize and apply the properties of the sides, angles, and diagonals of a parallelogram Recognize the conditions that ensure a quadrilateral is a parallelogram and prove that a set of points form a parallelogram in the coordinate plane Recognize and apply properties of rectangles and determine whether parallelograms are rectangles Recognize and apply properties of rhombi and squares and determine whether quadrilaterals are rectangles, rhombi, or squares Recognize and apply the properties of trapezoids, including the medians of trapezoids and recognize and apply the properties of kites Write ratios and write and solve proportions Use proportions to identify similar polygons and solve problems using the properties of similar polygons Identify similar triangles using the AA Similarity Postulate and use similar triangles to solve problems Use proportional parts with triangles and with parallel lines Recognize and use proportional relationships of corresponding segments of similar triangles and use the Triangle Angle Bisector Theorem Find the geometric mean between two numbers and solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse Use the Pythagorean Theorem and the Converse of the Pythagorean Theorem Use the properties of 45 Â -45 Â -90 Â triangle and the 30 Â -60 Â -90 Â triangles Find the trigonometric ratios using right triangles and use trigonometric ratios to find angle measures in right triangles Solve problems involving angles of elevation and depression and use to find the distance between two objects Use the Law of Sines and Cosines to solve triangles Find the magnitudes and directions of vectors and add and subtract vectors Draw reflections and draw reflections in the coordinate plane Draw translations and draw translations in the coordinate plane Draw rotations and draw rotations in the coordinate plane Identify and sketch solids formed by revolving tow-dimensional figures about lines Draw glide reflections and other compositions of isometries in the coordinate plane and draw compositions of reflections in parallel and intersecting lines Identify line and rotational symmetries in two-dimensional figures and identify plane and axis symmetries in three-dimensional figures Draw dilations and draw dilations in the coordinate plane Identify and use parts of circles and solve problems involving the circumference of a circle Identify central angles, major and minor arcs, and semicircles, and find their measures Recognize and use relationships between arcs, chords, and diameters Find measures of inscribed angles and measures of angles on inscribed polygons Use properties of tangents and solve problems involving circumscribed polygons
4 Find measures of angles formed by lines intersecting on or inside a circle and of angles formed by lines intersecting outside the circle Find measures of segments that intersect in the interior and exterior of a circle Write the equation of a circle and graph a circle on the coordinate plane Find perimeters and areas of parallelograms and triangles Find areas of trapezoids, rhombi, and kites Find areas of circles and find areas of sectors of circles Find areas of regular polygons and composite figures Find areas of similar figures by using scale factors and find scale factors or missing measures given the areas of similar figures Draw isometric views and investigate cross sections of three-dimensional figures. Find lateral areas and surface areas of prisms, cylinders, pyramids, and cones Find volumes of prisms, cylinders, pyramids, and cones Find surface areas and volumes of spheres Describe sets of points on a sphere and compare and contrast Euclidean and spherical geometries Identify congruent or similar solids and use properties of similar solids Represent sample spaces and use the Fundamental Counting Principle to count outcomes Use permutations and combinations with probability Find probabilities by using length and area Design simulations to estimate probabilities and summarize data from simulations Find probabilities of independent and dependent events and given the occurrence of other events Find probabilities of events that are mutually exclusive and events that are not mutually exclusive, and of complements Assignment(s): Students will begin each chapter (module) with some of an "Are YOU Ready?" quiz. Each module will also require the Visualize Vocabulary assignment and will conclude with a chapter test. All lessons will require the "YOUR TURN" section problems to be filled in during direct instruction. Some guided and independent practice problems will be required as well as H.O.T. (higher order thinking) problems for each lesson. Unit Assignment(s): Assignment(s): Students will begin each chapter (module) with some of an "Are YOU Ready?" quiz. Each module will also require the Visualize Vocabulary assignment and will conclude with a chapter test. All lessons will require the "YOUR TURN" section problems to be filled in
5 during direct instruction. Some guided and independent practice problems will be required as well as H.O.T. (higher order thinking) problems for each lesson. Course Materials Websites Title Kahn Academy Author(s)/Editor(s)/Compiler(s) Affiliated Institution or Organization URL [ empty ] Kahn Academy
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