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Fayette County Public Schools Geometry Curriculum Map (Long Range Plans) SEMESTER 1 (KCAS) Topic ***CLICK HERE FOR ALL POSTULATES & THEOREMS LISTED WITHIN DOCUMENT*** Procedures and Expectations Solving algebraic equations, simplifying algebraic expressions 1 2 3 BIG IDEAS (UNIT 1A) BASICS OF GEOMETRY Section (Prentice Hall) Know precise definitions of angles, lines, segments, parallel, and perpendicular based on undefined notions of point, line, and plane. Prove and use theorems and definitions about angles (vertical, complementary, supplementary, etc.) Find the lengths of line segments and the measures of angles. Determine if segments or angles are congruent. 4 G.CO.1 5 G.CO.1 Identify and describe collinear, coplanar points, and intersecting lines, identify basic geometric symbols, correctly name geometric figures Describe the difference between a theorem and a postulate , use the Segment Addition Postulate to find the measure of a segment, accurately measure a segment with a ruler, copy a segment using construction tools 1.2 1.2/1.3 1.3/1.5 1.4/1.5 6** G.CO.12 Find the midpoint between two points, applications of using the distance formula (find the distance between two points, Pythagorean Theorem, perimeter, etc.), bisect a segment using construction tools 1.3/1.5 1.5/1.6 7 G.CO.9 Classify angles as right, acute, obtuse, or straight, use the Angle Addition Postulate to find the measure of an angle, accurately measure an angle with a protractor, copy an angle using construction tools 1.4/1.5 1.4/1.5 8 G.CO.9 9 G.CO.9 10 11 Solve problems involving angle bisectors, bisect an angle using construction tools 1.5 1.5 1.6/2.6 2.5 Identify and sketch examples of vertical angles and linear pairs, solve problems involving the measures of vertical angles and linear pairs, solve problems involving complementary and supplementary angles Review Exam Unit 1A: Vocabulary Prerequisite Skills Section (McDougalLittell) Points, space, line, collinearity, plane, coplanar, postulate, axiom Segment, ray, opposite rays, parallelism, skew lines Coordinate, congruent segments, midpoint, angle, acute, right, obtuse, straight, congruent angle Vertical angles, adjacent, complementary, supplementary, theorem, proof Absolute value Solving and writing linear equations Solving and writing systems of linear equations Postulate 1.8 Theorems and Postulates (see link at top) Postulates 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8 Theorems 2.1, 2.2, 2.3, 2.4, 2.5 BIG IDEAS (UNIT 1B) TRANSFORMATIONS Represent transformations in the plane using a variety of methods. Describe rotations and reflections that carry a polygon onto it. Use developed definitions of rotations, reflections and translations in terms of angles, circles, lines, and segments. Draw a transformed figure (by rotating, reflecting, translating) using a variety of methods. 12 G.CO.2 Describe rigid motions in a plane, identify the three basic rigid transformations 7.1 12.1-12.3 13 G.CO.3 Describe a reflection, identify lines of reflectional symmetry, perform reflections in the coordinate plane (include the line y = x) 7.2 12.1 14 G.CO.4 Describe a rotation, identify lines of rotational symmetry, perform rotation in the coordinate plane about the origin and other points 7.3 12.3/12.5 15 G.CO.5 Describe a translation, perform translations in the coordinate plane 7.4 12.2 16 G.CO.2 Describe a glide reflection, describe a composition, perform compositions of transformations, review 7.5 12.4 17 Finish review, Exam Unit 1B: Vocabulary Prerequisite Skills Preimage, image, isometry, reflection, transformation, rigid Translation, composition, vector notation Rotation Glide reflection Drawing reflections and compositions Theorems and Postulates (see link at top) Formative Assessment Lessons (FALs) (click links below) Theorems 12.1, 12.2, 12.3, 12.4, 12.5 Transforming 2D Figures BIG IDEAS (UNIT 1C) PARALLEL AND PERPENDICULAR LINES 18 G.CO.1 G.CO.9 19 G.CO.9 20 G.CO.12 21 ** G.GPE.5 22 23 Identify angles formed by two lines cut by a transversal. Prove that when parallel lines are cut by a transversal that alternate interior angles, corresponding angles, alternate exterior angles are congruent; same side interior are supplementary. Use properties of parallel lines to determine if lines are perpendicular. Identify parallel, perpendicular, and skew lines, identify four pairs of angles formed by transversals (City Designer Activity) 3.1 1.3/3.1-3.2 Solve problems involving the measures of special angle pairs 3.3 3.1/3.2 Prove, by angle measurements, that two lines are parallel, construct a parallel line through a point not on a given line using construction tools Use the slope formula to find the slope of a line between two points, use slope to identify parallel and perpendicular lines in the coordinate plane Review Exam 3.4 3.7 3.6/3.7 3.5-3.6 Unit 1C: Vocabulary Prerequisite Skills Transversal, alternate interior, exterior, same-side interior (consecutive), corresponding Acute triangle, right triangle, obtuse triangle, equilateral triangle, equiangular triangle, scalene triangle, isosceles triangle, exterior angles of a polygon, remote interior angles Polygon, convex, concave, equilateral, equiangular, regular polygon Solving and writing linear equations Theorem 2.1 Postulate 1.8 Converses Theorem 3.7 Theorems and Postulates (see link at top) Postulates 3.1, 3.2 Theorems 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.10 BIG IDEAS (UNIT 1D) TRIANGLE CONGRUENCY 24 G.CO.10 25 G.CO.6 G.CO.7 G.CO.8 26 G.CO.8 27 G.CO.10 28 G.CO.10 29 G.CO.10 30 G.CO.10 31 G.CO.10 32 33 Use rigid motion to show that triangles are congruent. Explain why triangles are congruent using ASA, AAS, SAS, SSS, and HL. Use CPCTC to show parts of triangles congruent. Show base angles of an isosceles triangle are congruent and use this fact to solve problems. Recognize congruent triangles and their parts in overlapping figures. Use the fact that a point on a perpendicular bisector is equidistant to the endpoints of the bisected segment to solve problems. Use midsegments to find angle measures and side lengths. Use properties of altitudes, angle bisectors and medians to solve problems. Find the point at which medians, altitudes, or bisectors meet and use these points to solve problems. Use triangle inequality to make conjectures about sides and angles in triangles. Use the triangle angle sum theorem and exterior angle sum theorem to solve problems. Classify triangles based on angle measure, use the triangle sum theorem and exterior angle 4.1 3.3 theorem to solve triangles Introduce congruence in terms of Transformations. Determine if triangles are congruent, write 4.2 4.1-4.3 congruence statements Determine if triangles are congruent, prove that triangles are congruent using various postulates/theorems Use theorems to prove triangles are congruent, use the H-L theorem to prove triangles congruent, use the base angle theorem (and converse) to prove triangles are congruent Define a bisector, bisect a segment using construction tools, bisect an angle using construction tools, find the missing sides of a triangle using bisectors Define the median and altitude of a triangle, construct the median and altitude or a triangle 4.3/4.4 4.1-4.3 4.6 4.1-4.3/4.6 5.1/5.2 1.5 5.3 5.3 Find the midsegment of a triangle 5.4 5.1 Determine if three sides form a triangle, construct a triangle given three sides 5.5 5.5 Review Exam (Intro to next unit: Classify polygons) 6.1 3.4 Unit 1D: Vocabulary Prerequisite Skills Congruent polygons Legs, base, vertex angle, base angles for isosceles triangles, corollary Midsegment Distance from a point to a line Median, centroid, altitude Solving and writing linear equations Identifying angle pairs Theorem 4.1 Postulates 4.1, 4.2 Listing congruent parts (CPCTC) Finding slope Finding midpoint Theorems and Postulates (see link at top) Formative Assessment Lessons (FALs) (click links below) Theorems 4.1, 4.2, 4.3, 4.4, 4.5 Postulates 4.1, 4.2, 4.3 Corollaries to 4.3, 4.4 Theorems 5.1, 5.2, 5.3, 5.4, 5.5, 5.8 Analyzing Congruence Proofs BIG IDEAS (UNIT 1E) QUADRILATERALS 34 G.CO.11 35 G.CO.11 36 G.CO.11 37 G.CO.11 38 G.GPE.7 39 40 Recognize and sort quadrilaterals by their properties. Use properties of parallelograms to solve problems (opposite sides congruent, opposite angles congruent, diagonals bisect each other, rectangles have congruent diagonals) Prove a quadrilateral is a parallelogram. Determine if a parallelogram is a square or rectangle. Use properties of squares, rectangles, trapezoids, and kites to solve problems. Find the measures of interior and exterior angles of polygons. Intro to Quadrilaterals—properties and find the sum of interior angles (polygon formulas) 6.1 3.4/6.1 Use the properties of parallelograms to solve for x and y 6.2 6.2-6.4 Use the properties of rectangles, rhombi, and squares to solve for x and y 6.4 6.4 Prove a quadrilateral is a parallelogram based on angle measures Area and perimeter of quadrilaterals Review Exam Unit 1E: Vocabulary Prerequisite Skills Theorems and Postulates Parallelogram, rhombus, rectangle, square, trapezoid, isosceles trapezoid, kite Consecutive angles 41 42 Solving and writing linear equations Solving and writing linear equations Theorem 3.9 Finding midpoint Theorem 2.1 Theorem 3.1 Theorem 2.1 Theorem 3.1 Theorem 3.7 Final Exam Review Final Exam ** indicates a day that can be moved to second semester if needed Theorems 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 6.10, 6.11, 6.12, 6.13, 6.14 Formative Assessment Lessons (FALs) (click links below) Evaluating Statements About Length and Area SEMESTER 2 (KCAS) BIG IDEAS (UNIT 2A) SIMILARITY 1 G.SRT.2 2 G.SRT.1 3 G.SRT.3 4 G.SRT.3 5 G.SRT.4 6 G.SRT.5 7 8 G.SRT.8 Topic Section (ML) Use dilations to define and explain similarity. (angles congruent, sides proportional) Determine if two triangles are similar and if so write similarity statements. Prove triangles similar by AA, SAS, and SSS and use proportions to find the length of a missing side. Use the geometric mean to find the length of a missing side in a right triangle with altitude drawn to hypotenuse. Use the side-splitter theorem and triangle angle bisector theorem to solve problems. Introduction to Similarity—Solve word problems involving ratio & proportion, state properties of 8.1/8.2 similar figures Describe a dilation, dilate a figure in the coordinate plane 8.7 Find missing values (sides/angles) in similar figures Section (PH) 8.1-8.2 12.7 8.3/8.4 8.1-8.2 Prove that triangles are similar & Quiz 8.5 8.3 Use the proportionality theorems to find missing values in similar triangles 8.6 8.5 Solve problems involving similar right triangles (geometric mean/altitude to the hypotenuse) 9.1 8.4 Review Exam & Introduction to solving right triangles using Pythagorean Theorem 9.2 7.2 Unit 2A: Vocabulary Prerequisite Skills Cross-product property Extended proportion Geometric mean Golden Ratio and Rectangle Indirect Measurement Proportion Ratio Scale, scale drawing, scale factor Similar Similarity Ratio Simplifying expressions Midsegments Congruency Congruency Postulates Medians Altitudes Perimeter and area Theorems and Postulates (see link at top) Formative Assessment Lessons (FALs) (click links below) Postulate 8.1 Theorems 8.1, 8.2, 8.3, 8.4, 8.5, 8.6 Corollaries to 8.3, 8.4 Solving Geometry Problems: Floodlights BIG IDEAS (UNIT 2B) RIGHT TRIANGLE TRIGONOMETRY 9 10 G.SRT.6 11 G.SRT.6 12 G.SRT.6 13 G.SRT.6 14 G.SRT.7 15 G.SRT.8 16 17 Use the Pythagorean Theorem to solve problems. Use special triangles (3-4-5, 7-24-25, 5-12-13, 8-15-17, 30⁰-60⁰-90⁰, 45⁰-45⁰-90⁰) to solve for missing sides in right triangles. Use trigonometric ratios to solve problems. Use simple properties of trig ratios (ex. sine ratio to find cosine of complementary angles, trig ratios are equal in similar triangles. Solve indirect measurement problems using trigonometry. Simplify radicals and radical expressions (include all operations) 9.2 7.1 (addendum to 7.1 on p 355 (alg 1 review) Use the Pythagorean Theorem to solve for missing sides in a right triangle, use the converse of the 9.2/9.3 7.2 Pythagorean Theorem to determine if a triangle is acute, right, or obtuse Solve special right triangles (45-45-90 and 30-60-90) 9.4 7.3 Quiz and find trigonometric ratios in a right triangle 9.5 9.1-9.2 Solve for missing sides in right triangles using trig ratios (include applications) 9.5 9.1-9.3 Solve word problems using trigonometry, use the inverse to solve right triangles (include applications) Review Exam 9.6 9.1-9.3 Unit 2B: Vocabulary Prerequisite Skills Angles of Depression and Elevation SohCahToa Initial and terminal point Writing and solving equations Solving proportions Simplifying radicals Writing ratios Finding measures of angles Triangle angle sum theorem Theorems and Postulates (see link at top) Formative Assessment Lessons (FALs) (click links below) Theorems 7.4, 7.5, 7.6, 7.7, 7.8, 7.9 Geometry Problems: Circles and Triangles Proofs of the Pythagorean Theorem BIG IDEAS (UNIT 3) VOLUME 18 G.GMD.4 19 G.GMD.4 20 G.GMD.1, G.GMD.3 21 G.GMD.1, G.GMD.3 22 G.GMD.1, G.GMD.3 23 Master finding the area of a two dimensional figure. Find the surface area of a 3 dimensional figure. Find the volume of a cylinder, pyramid, cone or sphere. Find the 2 dimensional cross section of a three dimensional object and find the 3 dimensional object based on the rotation of a two dimensional figure. Know the relationship between perimeter, area, and volume involving the ratio of sides Introduction to 3-dimensional figures—naming solids, identifying edges, faces, and vertices 10.1/supplement (Euler’s Theorem), rotating a 2D figure about an axis to create 3D figures, review of perimeter and 12.1 plane area 10.1/supplement Find the volume of a prism and cylinder 12.4 10.5 Find the volume of a pyramid and cone 12.5 10.6 Find the volume of a sphere, and review 12.6 10.7 Exam Unit 3: Vocabulary Prerequisite Skills Solid Altitude and Slant height Base Cone Cross-section Cylinder Prism Pyramid Sphere Volume Edge, face, vertices Rotation about axis Area Perimeter and circumference Pythagorean Theorem Solving and writing equations Theorems and Postulates (see link at top) Formative Assessment Lessons (FALs) (click links below) Theorems 10.1, 10.2, 10.5, 10.6, 10.7, 10.8, 10.9, 10.11, 10.12 2D Representations of 3D Objects Calculating Volumes of Compound Objects Evaluating Statements About Enlargements (2D and 3D) BIG IDEAS (UNIT 4) COORDINATE GEOMETRY 24 G.GPE.7 25 G.GPE.5 26 G.GPE.4 27 G.GPE.4 28 G.GPE.4, G.GPE.1 29 G.GPE.2, G.GPE.1 30 31 Use distance and midpoint formulas to find length and midpoint of a segment in the coordinate plane Use coordinate geometry to determine the type of quadrilateral Use coordinate geometry to prove theorems about 2 dimensional figures Determine and write equations of circles and parabolas Find the slope between two points, find the distance between two points, and find the midpoint of two points Write the equation of a line (include parallel and perpendicular lines) Quiz and use formulas (from day 23) to solve triangle problems in the coordinate plane (prove a triangle is equilateral, right, etc.) Use formulas (from day 23) to solve quadrilateral problems in the coordinate plane (prove a quadrilateral is a rectangle, square, etc.) Write equations of circles given the center and radius, graph a circle, prove a point is on a circle in the coordinate plane **can be moved to beginning of circles unit Write the standard form equation of a parabola given the vertex, directrix, and/or focus. 3.5 3.6 Supplement 6.3 10.6 11.5 Supplement Review Exam Unit 4: Vocabulary Prerequisite Skills Slope, distance, midpoint Slope-intercept form Point-slope form Parallel and perpendicular Center, radius, diameter Circle Parabola Vertex, focus, directrix Solving and writing equations Reciprocals Graphing a point Graphing horizontal and vertical lines Theorems and Postulates (see link at top) Formative Assessment Lessons (FALs) (click links below) Theorems 6.6, 6.7, 6.8, 11.13 Equations of Circles 1 Equations of Circles 2 Finding Equations of Parallel and Perpendicular Lines BIG IDEAS (UNIT 5) CIRCLES 32 G.C.1, G.C.2, G.C.4 33 G.C.4 34 G.C.5 35 G.C.2, G.C.3 36 G.C.5 37 38 Prove that all circles are similar Identify and use relationships among inscribed angles, radii, and chords Construct circumscribed and inscribed circles on a triangle and use them to describe properties of angles of a quadrilateral Construct tangent lines to a circle Show that the arc intercepted by an angle is proportional to the radius Identify, sketch, and/or define segments related to a circle (radius, diameter, tangent, secant, etc.), 10.1/10.2 7.6 identify and name arcs of a circle (major, minor, semicircle), construct a line tangent to a circle from a point not on the circle, prove all circles are similar Determine whether or not a line is tangent to a circle, solve problems involving tangent segments drawn to an external point, find the measures of tangent-tangent angles and their intercepted arcs Find the measure of central angles, find the measure of intercepted arcs 11.1 Solve problems involving inscribed angles (including angles inscribed in a semicircle are right angles), construct the inscribed and circumscribed circles of a triangle Find arc length and sector area of a circle 11.3 11.4 7.6/7.7 Review Exam & Intro to Probability (Use the Fundamental Counting Principle to count the number of ways an event can happen) Unit 5: Vocabulary Prerequisite Skills Circumscribe Inscribe Arc Point of tangency Secant Equation of circle Tangent to circle Sector 11.2 Naming, finding angles Angle addition Circumference Area Theorems and Postulates (see link at top) Formative Assessment Lessons (FALs) (click links below) Postulate 7.1 Theorem 7.14, 7.16, 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7, 11.8, 11.9, 11.10 Inscribing and Circumscribing Right Triangles BIG IDEAS (UNIT 6) PROBABILITY 39 S.CP.9 40 S.CP.2 41 S.CP.2 42 S.CP.2 43 S.CP.3, S.CP.4, S.CP.5, S.CP.6 44 Describe the sample space of an event using unions, intersection, complements Determine probability of independent events Understand the concepts of conditional probability and find conditional probabilities Use two way frequency tables to approximate probabilities Use probability to make decisions on fairness of a situation Use counting techniques to solve problems (include combinations and permutations) MILC Calculate simple probability (include complements) MILC Probability of Multiple Events –include dependent/independent events, mutually/non-mutually exclusive events, and unions/intersections MILC Conditional Probability PH Algebra 2 (11.2) Quiz Unit 6: Vocabulary Prerequisite Skills Theorems and Postulates Sample space Union Intersection Complement Probability Independent event Conditional probability Two-way frequency table Permutations and combinations Mutually exclusive 45 46 Final Exam Review Final Exam Ratios Percent MILC Formative Assessment Lessons (FALs) (click links below) Modeling Conditional Probabilities 1: Lucky Dip Modeling Conditional Probabilities 2