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High School Geometry A Content/Topics Skills/Process Chapter 1: Lines and Angles Points, lines, and planes Linear measure and precision Distance and midpoints Angle measure Angle relationships Polygons Chapter 2: Reasoning and Proof Inductive reasoning and proof Logic Conditional statements Deductive statements Postulates and paragraph proof Algebraic proof Proving segment relationships Proving angle relationships Chapter 3: Parallel and Perpendicular Lines Parallel lines and transversals Angles and parallel lines Slopes of lines Equations of lines Proving lines parallel Perpendiculars and distance Chapter 4: Congruent Triangles Classify triangles Angles of triangles Proving congruence Isosceles triangles Triangles and coordinate proof Identify and model points, lines, planes, collinear and coplanar points, and intersecting lines Measure segments, compute with measures, and determine accuracy Find distance and midpoint Measure and classify angles Identify special pairs of angles Perpendicular lines Identify, name, and find perimeter of polygons Use geometry tools Inductive reasoning and counterexamples Truth values and tables If-then statements, converse, inverse, contrapositive Law of Detachment and Syllogism Use postulates to write paragraph proofs Use algebra to write two-column proofs Write proofs involving segment addition and congruence Write proofs involving supplementary and complementary angles and congruent and right angles Angle pairs formed by parallel lines and transversals Parallel lines and congruent angles Slopes of lines, parallel and perpendicular lines Write equation of line Prove lines are parallel Find distance between point and line and distance between parallel lines Identify and classify triangles by angles and sides Angle Sum Theorem Exterior Angle Theorem Corresponding parts of congruent triangles Test for congruent triangles: SSS, SAS, ASA, AAS Properties of isosceles and equilateral triangles Position and label triangles for coordinate proofs Write coordinate proofs Assessment/ Products Quiz Test MCA/GRAD Benchmarks V.B.3 V.B.5 V.B.7 V.B.8 Quiz Test Quiz Test V.B.1 V.B.5 V.C. Quiz Test V.B.1 11/21/2007 High School Geometry B Content/Topics Skills/Process Chapter 5: Relationships in Triangles Bisectors, medians, and altitudes Inequalities and triangles Triangle inequalities Inequalities involving two triangles Chapter 6: Proportions and Similarity Similar polygons Similar triangles Parallel lines and proportional parts Parts of similar triangles Chapter 7: Right Triangles and Trigonometry Geometric mean Pythagorean theorem and its converse Special right triangles Trigonometry Angles of elevation and depression Law of Sines and Law of Cosines Chapter 8: Quadrilaterals Angles of polygons Parallelograms Tests for parallelograms Rectangles Rhombi and squares Trapezoids Coordinate proof with quadrilaterals Perpendicular bisectors, angle bisectors, medians, and altitudes Relationships between angle measures and sides in a triangle Triangle Inequality Theorem Identify shortest distance between point and line SAS and SSS Inequality Write ratios and solve problems Identify similar figures and triangles Solve problems involving scale factors and similar triangles Proportional parts of triangles Recognize and use proportional relationships of corresponding perimeters, angle bisectors, altitudes, and medians of similar triangles Find geometric mean and solve problems between parts of right triangles Pythagorean theorem and its converse Use properties of 45-45-90 degree triangles Use properties of 30-60-90 degree triangles Find trig ratios and solve problems Solve problems involving angles of elevation and depression Use Law of Sines and Cosines and solve problems Find sum of measures of interior and exterior angles Recognize and apply properties of the sides, angles, and diagonals of parallelograms Prove quadrilaterals are parallelograms Recognize and apply properties of rectangles, rhombi, squares, and trapezoids Solve problems with quadrilaterals Coordinate proofs with quadrilaterals Assessment/ Products MCA/GRAD Benchmarks Quiz Test Quiz Test Quiz Test Quiz Test V.B.1 V.C.G1 V.B.3 V.B.4 V.B.1 V.B.3 11/21/2007 Chapter 9: Transformations Reflections Translations Rotations Tessellations Dilations Vectors Draw reflected images, lines of symmetry, and points of symmetry Draw translated, rotated, and dilated images Identify regular tessellations Find magnitudes and directions of vectors and perform translations Quiz Test V.B.6 11/21/2007 High School Geometry C Content/Topics Skills/Process Chapter 10: Circles Circles and circumference Angles and arcs Arcs and chords Inscribed angles Tangents Secants, tangents, and angle measures Equation of circles Chapter 11: Areas of Polygons and Circles Areas of parallelograms Areas of triangles, trapezoids, and rhombi Areas of regular polygons and circles Areas of irregular figures Geometric probability Chapter 12: Surface Area Three-Dimensional figures Nets and surface area Surface areas of prisms Surface area of cylinders Surface area of pyramids Surface area of cones Surface area of spheres Identify and use parts of circles Solve problems involving circumference Recognize and find measure of major arcs, minor arcs, semicircles, and central angles Recognize and use relationships between arcs and chords and chords and diameters Find measures of inscribed angles and angles of inscribed polygons Use properties of tangents and solve problems involving circumscribed triangles Find measures of angles formed by lines intersecting on, inside, or outside a circle Find measures of segments that intersect in the interior or exterior of a circle Write equation of circle an graph on coordinate plane Find perimeters and areas of parallelograms, triangles, trapezoids, regular polygons, circles, and irregular figures Solve problems involving geometric probability, sectors and segments of circles Identify, make, and use three-dimensional figures Draw two-dimensional models for three-dimensional figures Find lateral area and surface area of prisms, cylinders, pyramids, cones, and spheres Recognize basic properties of spheres Assessment/ Products MCA/GRAD Benchmarks Quiz Test V.B.2 V.B.7 V.C.G2 Quiz Test V.B.3 V.C.8 V.C.G2 Quiz Test V.A.1 V.B.3 V.C.G2 11/21/2007 Chapter 13: Volume Volumes of prisms and cylinders Volumes of pyramids and cones Volumes of spheres Congruent and similar solids Coordinates in space Find volumes of prisms, cylinders, pyramids, cones, and spheres Identify congruent or similar solids and know properties Graph solids in space Use the distance and midpoint formulas for points in space Quiz Test V.A.1 V.B.3 V.C.G1 V.C.G2 11/21/2007
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