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INDIANA DRAFT – MATHEMATICS – DRAFT LIST OF TERMS AND CONCEPTS FOR GEOMETRY BY MCREL NOVEMBER 2001 Summary of Standards for Geometry Standard 1 Points, Lines, Angles, and Planes Students find lengths and midpoints of lines. They describe and use parallel and perpendicular lines. They find slopes and equations of lines. Standard 2 Polygons Students identify and describe polygons, and measure interior and exterior angles. They use congruence, similarity, symmetry, tessellations, and transformations. They find measures of sides, perimeters, and areas. Standard 3 Quadrilaterals Students identify and describe simple quadrilaterals. They use congruence and similarity. They find measures of sides, perimeters, and areas. Standard 4 Triangles Students identify and describe types of triangles. They identify and draw altitudes, medians, and angle bisectors. They use congruence and similarity. They find measures of sides, perimeters, and areas. They apply inequality theorems. Standard 5 Right Triangles Students prove the Pythagorean Theorem and use it to solve problems. They define and apply the trigonometric relations sine, cosine, and tangent. Standard 6 Circles Students define ideas related to circles: e.g., radius, tangent. They find measures of angles, lengths, and areas. They prove theorems about circles. They find equations of circles. Standard 7 Polyhedra and Other Solids Students describe and make polyhedra and other solids. They describe relationships and symmetries, and use congruence and similarity. Standard 8 Mathematical Reasoning and Problem Solving Students use a variety of strategies to solve problems. Students develop and evaluate mathematical arguments and proofs. Standard 1 Points, Lines, Angles, and Planes Students find lengths and midpoints of lines. They describe and use parallel and perpendicular lines. They find slopes and equations of lines. Find the lengths and midpoints of line segments in one- or two-dimensional coordinate systems. length of a line segment midpoint of a line segment one-dimensional coordinate system two-dimensional coordinate system Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass, explaining and justifying the process used. angle [d] angle bisector [d] parallel lines [d] perpendicular lines [d] congruency [d] congruent segments congruent angles straight edge compass Understand and use the relationships between special pairs of angles formed by parallel lines and transversals. transversal angle [d] parallel lines [d] Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines. coordinate geometry [d] parallel lines [d] perpendicular lines [d] slope [d] equation of a line [d] [d] = Term or concept is duplicated within or among high school course(s) PAGE 1 DRAFT – MATHEMATICS: TERMS AND CONCEPTS FOR GEOMETRY – DRAFT Standard 2 Polygons Students identify and describe polygons, and measure interior and exterior angles. They use congruence, similarity, symmetry, tessellations, and transformations. They find measures of sides, perimeters, and areas. Identify and describe convex, concave, and regular polygons. convex polygon concave polygon regular polygon Find measures of interior and exterior angles of polygons, justifying the method used. interior angle exterior angle Use properties of congruent and similar polygons to solve problems. congruency [d] similarity [d] Apply transformations (slides, flips, turns, expansions, and contractions) to polygons in order to determine congruence, similarity, symmetry, and tessellations. Know that images formed by slides, flips and turns are congruent to the original shape. transformation slide (translation) flip (reflection) turn (rotation) similarity [d] symmetry expansion/contraction (dilation) tessellation congruency [d] Find and use measures of sides, perimeters, and areas of polygons, and relate these measures to each other using formulas. perimeter area [d] side of a polygon formula for perimeter of a polygon [d] = Term or concept is duplicated within or among high school course(s) PAGE 2 DRAFT – MATHEMATICS: TERMS AND CONCEPTS FOR GEOMETRY – DRAFT formula for area of a polygon perimeter of a polygon area of a polygon Use coordinate geometry to prove properties of polygons such as regularity, congruence, and similarity. coordinate geometry [d] congruency [d] similarity [d] Standard 3 Quadrilaterals Students identify and describe simple quadrilaterals. They use congruence and similarity. They find measures of sides, perimeters, and areas. Describe, classify, and understand relationships among the quadrilaterals square, rectangle, rhombus, parallelogram, trapezoid, and kite. kite quadrilateral [d] square rectangle rhombus parallelogram trapezoid Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas. length area [d] congruent quadrilaterals similar quadrilaterals Find and use measures of sides, perimeters, and areas of quadrilaterals, and relate these measures to each other using formulas. perimeter [d] area [d] formula for perimeter of a quadrilateral formula for area of a quadrilateral perimeter of a quadrilateral area of a quadrilateral [d] = Term or concept is duplicated within or among high school course(s) PAGE 3 DRAFT – MATHEMATICS: TERMS AND CONCEPTS FOR GEOMETRY – DRAFT Use coordinate geometry to prove properties of quadrilaterals such as regularity, congruence, and similarity. coordinate geometry [d] congruency [d] similarity [d] quadrilateral [d] Standard 4 Triangles Students identify and describe types of triangles. They identify and draw altitudes, medians, and angle bisectors. They use congruence and similarity. They find measures of sides, perimeters, and areas. They apply inequality theorems. Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular. triangle right triangle [d] acute triangle obtuse triangle scalene triangle isosceles triangle equilateral triangle equiangular triangle Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors. altitude [d] angle bisector [d] perpendicular bisector median of a shape Construct triangles congruent to given triangles. triangle [d] congruent triangles [d] Use properties of congruent and similar triangles to solve problems involving lengths and areas. triangle [d] congruent triangles [d] similar triangles [d] = Term or concept is duplicated within or among high school course(s) PAGE 4 DRAFT – MATHEMATICS: TERMS AND CONCEPTS FOR GEOMETRY – DRAFT Prove and apply theorems involving segments divided proportionally. theorem [d] proportional segment division Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles. triangle [d] congruent triangles [d] congruency [d] Find measures of sides, perimeters, and areas of triangles, and relate these measures to each other using formulas. triangle [d] formula for perimeter of a triangle formula for area of a triangle Prove, understand, and apply the inequality theorems: triangle inequality, inequality in one triangle, and hinge theorem. triangle [d] triangle inequality theorem inequality in one triangle theorem hinge theorem Use coordinate geometry to prove properties of triangles such as regularity, congruence, and similarity. triangle [d] coordinate geometry [d] congruency [d] similarity [d] Standard 5 Right Triangles Students prove the Pythagorean Theorem and use it to solve problems. They define and apply the trigonometric relations sine, cosine, and tangent. Prove and use the Pythagorean Theorem. Pythagorean Theorem [d] [d] = Term or concept is duplicated within or among high school course(s) PAGE 5 DRAFT – MATHEMATICS: TERMS AND CONCEPTS FOR GEOMETRY – DRAFT State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. triangle [d] hypotenuse altitude [d] Use special right triangles (30° - 60° and 45° - 45°) to solve problems. triangle [d] 30-60-90 special right triangle 45-45-90 special right triangle Define and use the trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) in terms of angles of right triangles. trigonometric function [d] sine function [d] cosine function [d] tangent function [d] cosecant function [d] secant function [d] cotangent function [d] right triangle [d] angle [d] Know and use the relationship sin2 x + cos2 x = 1. sin2 x + cos2 x = 1 [d] Solve word problems involving right triangles. right triangle [d] = Term or concept is duplicated within or among high school course(s) PAGE 6 DRAFT – MATHEMATICS: TERMS AND CONCEPTS FOR GEOMETRY – DRAFT Standard 6 Circles Students define ideas related to circles: e.g., radius, tangent. They find measures of angles, lengths, and areas. They prove theorems about circles. They find equations of circles. Find the center of a given circle. Construct the circle that passes through three given points (not in a straight line). circle [d] center of a circle [d] line Define and identify relationships among: radius, diameter, arc, measure of an arc, chord, secant, and tangent. diameter radius [d] chord [d] arc [d] measure of an arc [d] secant tangent [d] Prove theorems related to circles. circle [d] theorem [d] Construct tangents to circles, and circumscribe and inscribe circles. circle [d] tangent [d] circumscribed circle inscribed circle Define, find, and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents). angle [d] arc [d] measure of arc [d] central angle inscribed angle intersection of secants intersection of tangents [d] = Term or concept is duplicated within or among high school course(s) PAGE 7 DRAFT – MATHEMATICS: TERMS AND CONCEPTS FOR GEOMETRY – DRAFT Define and identify congruent, similar, and concentric circles. congruent circles similar circles concentric circles Define, find, and use measures of circumference, arc length, and areas of circles and sectors. Use these measures to solve problems. circle [d] circumference arc length sector of a circle area of a sector of a circle Find the equation of a circle in the coordinate plane in terms of its center and radius. radius [d] center of a circle [d] equation of a circle [d] Standard 7 Polyhedra and Other Solids Students describe and make polyhedra and other solids. They describe relationships and symmetries, and use congruence and similarity. Describe and make regular and non-regular polyhedra. polyhedron [d] regular polyhedron non-regular polyhedron Describe the polyhedron that can be made from a given net (or pattern). Describe the net for a given polyhedron. net polyhedron [d] [d] = Term or concept is duplicated within or among high school course(s) PAGE 8 DRAFT – MATHEMATICS: TERMS AND CONCEPTS FOR GEOMETRY – DRAFT Describe relationships between the faces, edges, and vertices of polyhedra. face [shape] edge [shape] vertex polyhedron [d] Describe symmetries of geometric solids. symmetries of solids Describe sets of points on spheres: chords, tangents, and great circles. sphere chord [d] great circle tangent [d] Identify and know properties of congruent and similar solids. congruent solids similar solids Standard 8 Mathematical Reasoning and Problem Solving Students use a variety of strategies to solve problems. Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and- check, solving a simpler problem, writing an equation, and working backwards. problem-solving strategy [d] guess-and-check [d] working backwards [d] Decide whether a solution is reasonable in the context of the original situation. reasonable solution [d] [d] = Term or concept is duplicated within or among high school course(s) PAGE 9 DRAFT – MATHEMATICS: TERMS AND CONCEPTS FOR GEOMETRY – DRAFT Students develop and evaluate mathematical arguments and proofs. Make conjectures about geometric ideas. Distinguish between information that supports a conjecture and proof of a conjecture. conjecture proof of a conjecture Write and interpret statements of the form “if – then” and “if and only if.” if-then (conditional) statement if and only if statement State, use, and examine the validity of the converse, inverse, and contrapositive of “if – then” statements. converse of “if-then” statement inverse of “if-then” statement contrapositive of “if-then” statement Identify and give examples of undefined terms, axioms, and theorems, and inductive and deductive proof. axiom theorem [d] inductive proof deductive proof [d] Construct logical arguments, judge their validity, and give counterexamples to disprove statements. logical argument valid argument counterexample Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow chart, paragraph, two- column, and indirect. geometric proof proof by contradiction coordinate proof deductive proof [d] flow chart proof paragraph proof two-column proof indirect proof [d] = Term or concept is duplicated within or among high school course(s) PAGE 10 DRAFT – MATHEMATICS: TERMS AND CONCEPTS FOR GEOMETRY – DRAFT Perform basic constructions, describing and justifying the procedures used. Distinguish between constructing and drawing geometric figures. construction of geometric figures [d] = Term or concept is duplicated within or among high school course(s) PAGE 11

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Euclidean geometry, projective geometry, Pythagorean Theorem, geometric figures, Geometry help, High School, geometric shapes, non-Euclidean geometry, solid geometry, Coordinate geometry

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posted: | 10/4/2010 |

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