TEACHER: Nelson/Ryalls/Ragan COURSE _Geometry I & II Curriculum Map

Transcription

1 SEPTEMBER understand how to apply geometry terms, postulates, and notation understand how to calculate segment and angle measurements understand how to do basic constructions with a compass and straight edge terms, postulates, and notation segment and angle measurement basic constructions OCTOBER understand how to apply conditionals, biconditionals, and laws of logic understand how to apply vertical, complementary, and supplementary angle relationships to problem-solving understand how to apply definitions and postulates to beginning proofs understand how to construct parallel and perpendicular lines with a compass and straight edge conditionals, bi-conditionals, and laws of logic angle relationships and problem-solving beginning proofs parallel and perpendicular line construction Make plausible connections based on observed patterns. Learn foundation blocks of Geometry Segment & Angle Measurement. Use of the coordinate plane and constructions to represent geometric figures. Write conditionals, bi-conditionals and definitions. Use statements and deductive reasoning to conclude statement truth. Apply deductive reasoning to Algebra. Use deductive reasoning to make conclusions about parallel & perpendicular lines. VOCABULARY Inductive reasoning, conjecture, counterexample, segment, ray, skew, parallel and perpendicular lines Conditional, hypothesis, conclusion, truth value, converse, biconditional, reflexive property, symmetric property, transitive property Curtis Junior High School 1

2 NOVEMBER understand how to solve problems(including proofs) involving angle relationships between parallel lines and polygons understand how to apply congruence postulates and theorems to determine triangle congruence angle relationships and isosceles triangles angles, parallel line, and polygon relationships proofs using congruent angles and alternate interior angles congruence postulates and theorems Use parallel lines to learn about angle measures in triangles and other polygons Learn to think about parallel and perpendicular lines in a coordinate plane. Learn the meaning of congruent polygons. Learn different methods to prove triangle congruence. Discover properties of isosceles triangles. DECEMBER understand how to complete proofs involving congruence and overlapping triangles proofs with congruence and overlapping triangles Learn how to draw conclusions once triangles have been proved congruent. VOCABULARY Vertical angles, adjacent, supplementary, and complementary angles, transversal, alternate interior angles, same side interior angles, Congruence, CPCTC, hypotenuse, legs of a triangle, vertex Curtis Junior High School 2

3 corresponding angles JANUARY understand how to perform calculations with midsections and bisectors FEBRUARY the Pythagorean Theorem special right triangles understand how to calculate the area of polygons understand how to calculate circumference, arc length, and arc measure understand how to calculate the area of circles, segments, sectors, and annuli midsections and bisectors Pythagorean Theorem special right triangles area of polygons circumference, arc length, and arc measure area of circles, segments, sectors, and annuli Learn about geometric relationships within triangles Become familiar with terminology. Apply indirect reasoning to deduce information about inequalities in triangles. Learn the Pythagorean Theorem and its converse Use the Pythagorean Theorem to find relationships in special triangles Learn how to find the areas of special quadrilaterals and regular polygons. VOCABULARY Altitude, centroid, circumcenter, incenter, orthocenter, midsegment, median, concurrent, point of concurrency Circumference, apothem, arc length, base, central angle, geometric probability, pi, radius, segment, sector, semicircle Curtis Junior High School 3

4 MARCH understand how to apply trigonometry ratios and their inverses to problem-solving understand how to solve problem with angles of elevation and depression understand how to calculate the area of polygons using trigonometry trig ratios and their inverses angles of elevation and depression area of polygons and trigonometry vectors Learn to use similar right triangles to define sine, cosine, and tangent ratios. Solve height and distance problems using angles of elevation and depression. Learn how to use vectors as a tools in other applications of trigonometry. APRIL similar polygons similarity in right triangles understand how to calculate the perimeter and area of similar polygons similar polygons right triangle similarity perimeter and area of similar polygons Learn that similar polygons have the same shape, but not necessarily size. Prove triangles similar Find additional relationships within triangles. Learn how the perimeters and areas of similar figures are related. VOCABULARY proportion, indirect measurement, angle of depression, angle of elevation, tangent, sine, cosine Similar, similarity ratio, golden ratio, golden rectangle, geometric mean Curtis Junior High School 4

5 MAY tangents, chords, arcs, and secants inscribed angles understand how to find angle measures and lengths formed by chords, secants, and tangents JUNE understand how to calculate the surface area and volume of pyramids, prisms, cylinders and cones tangents, chords and arcs inscribed angles arcs and lengths from chords and secants Learn the many properties of circles and the lines associated with circles. Learn how angles are related to arcs when they intercept circles. surface area and volume of prisms and cylinders Learn about special three-dimensional figures built from two-dimensional figures like triangles and rectangles Create three dimensional drawings on a two dimensional piece of paper. VOCABULARY Tangent, point of tangency, inscribed, circumscribed, chord, inscribed angle, intercepted arc, secant Altitude, base, cone, cube, cylinder, edge, face, hemisphere, lateral area, lateral faces, net, prism, pyramid, radius, slant height, similarity ratio, vertex, volume Curtis Junior High School 5