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Transcript

Developing Geometric Sense Transitions: Coordinate Plane. Equations of lines parallel and perpendicular to each other and a given line. Supplementary, complementary, vertical, and adjacent angles. Number patterns and inductive reasoning. Disproving statements using counter examples. Midpoints, angle bisectors, and the bisector of a segment. Construction of the perpendicular bisector of a line segment* Understand polygons and angles Understand parallel lines cut by transversals 12.0, 13.0, 16.0* 7.0, 16.0* Standards 1.0, 2.0, 3.0 Using axioms, theorems, definitions and examples Using inductive and deductive reasoning Proof by contradiction Constructing geometric proofs, logical arguments and counterexamples • Construct the bisector of an angle* • Construct an angle congruent to a given angle* • Solve problems using angle and side measures for triangles and polygons • Prove relationships between angles in polygons • Construct the parallel to a line through a point not on the line* • Prove and use properties of parallel lines cut by a transversal • Construct the perpendicular to a line from a point on the line and from a point not on the line* G E O M E T R Y Triangles, Trigonometry and Quadrilaterals Transitions: Similarity and congruence of common geometric figures using the coordinate system Use of the Pythagorean Theorem and its converse to find the length of the missing side of a right triangle Ratios and proportions Roots and radicals Simple properties of common quadrilaterals and triangles Construction of congruent triangles* Understand triangle congruency and similarity Understand the properties of quadrilaterals Understand the properties of right triangles and trigonometry 4.0, 5.0, 6.0, 16.0* 7.0 14.0, 15.0, 16.0*, 18.0, 19.0, 20.0 Standards 1.0, 2.0, 3.0 Using axioms, theorems, definitions and examples Using inductive and deductive reasoning Proof by contradiction Constructing geometric proofs, logical arguments and counterexamples • Prove congruence of triangles • Apply ratios and proportions to solving problems • Use the triangle inequality • Construct the circumcircle of a triangle* • Prove and use properties of quadrilaterals • Categorize shapes based on properties • Prove the Pythagorean Theorem • Use the Pythagorean Theorem to find missing sides and distance • Use special right triangle properties. ( 45° , 45° , 90° and 30°, 60°, 90° ) • Know and use trigonometric ratios G E O M E T R Y Circles, Area and Volume • Transitions: Circumference, radius, diameter, and pi Area and volume of common geometric figures Use of coordinate graphs to plot simple figures, determine related lengths and areas, and determine their image under translations and reflections Ratios and proportions Area of common geometric figures using the coordinate system Understand the properties of circles Understand, derive and apply area formulas Understand volume and surface area 7.0, 16.0*, 21.0 8.0, 10.0, 11.0 9.0, 11.0 Standards 1.0, 2.0, 3.0 Using axioms, theorems, definitions and examples Using inductive and deductive reasoning Proof by contradiction Constructing geometric proofs, logical arguments and counterexamples • Derive and solve problems involving circumference and area • Prove and solve problems about inscribed angles, chords, secants, tangents, inscribed and circumscribed polygons • Construct the tangent to a circle from a point on the circle* • Construct the tangents to a circle from a point not on the circle* • Use construction to locate the center of a circle* • Compute area of triangles and quadrilaterals • Solve problems involving perimeter and area • Investigate how dimension changes affect perimeter and area • Solve problems involving surface area • Solve problems involving volume • Investigate how dimension changes affect volume and surface area G E O M E T R Y Transformations and Coordinate Geometry • Transitions: Coordinate system Use of coordinate graphs to plot simple figures, determine related lengths and areas, and determine their image under translations and reflections Equations of lines Understand transformations 22.0 CST Understand the relationships in coordinate geometry 17.0 Standards 1.0, 2.0, 3.0 Using axioms, theorems, definitions and examples Using inductive and deductive reasoning Proof by contradiction Constructing geometric proofs, logical arguments and counterexamples • Rotate, translate, reflect, and stretch figures and objects • Prove theorems using elements of coordinate geometry such as: 1) midpoint formula 2) distance formula 3) equations of lines 4) equations of circles G E O M E T R Y