FONTANA UNIFIED SCHOOL DISTRICT Glencoe Geometry Quarter 1 Standards and Objectives Pacing Map

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1 Glencoe Geometry Quarter 1 1 August August *1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. *16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. Review & Pre-Assessment Tools of Geometry 1.1 Points, Lines, and Planes 1.2 Linear Measure and Precision 1.3 Distance and Midpoints 1.4 Angle Measure undefined terms, point, line, plane, collinear, coplanar, space segment, betweeness, congruent, constructions, distance, midpoint, segment bisector, angle bisector, ray, right angle, acute, obtuse, vertex 3 August Aug/Sept September Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric *10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. *1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. *3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. *1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. *3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. 1.5 Angle Relationships 1.6 Two-Dimensional Figures Algebra topics prerequisite for Chapter 2: Solve multi-step equations including those with fractions and grouping symbols. See Algebra I book sections 2-4 & 2-5. Reasoning & Proof 2.1 Inductive Reasoning and Conjecture 2.3 Conditional Statements 2.4 Deductive Reasoning 2.5 Postulates and Paragraph Proofs 2.6 Algebraic Proof adjacent angles, vertical angles, linear pair, complementary & supplementary angles, perpendicular lines polygon-regular, convex, concave, perimeter, circumference, area conjecture, inductive & deductive reasoning, counterexample, conditional, if-then statements, hypothesis, conclusion, converse, inverse, contrapositive point, line, plane postulates, proof components, Midpoint Theorem, Algebraic Properties Department of Secondary Instruction Page 1 of 8 Updated 7/8/10

2 Glencoe Geometry Quarter 1 6 September September Sept/Oct Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. 2.0 Students write geometric proofs, including proofs by properties of quadrilaterals, and the properties of circles. *16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 2.7 Proving Segment Relationships 2.8 Proving Angle Relationships Site Based Common Assessment Algebra topics prerequisite for Chapter 3: Derive the equation of a line. Determine if a point is a solution of a linear equation. Solve equations with variables on both sides of the equal sign. Solve equations with decimal coefficients. Solve systems of equations. See Algebra I book sections 4-4 & 4-5. Parallel and Perpendicular Lines 3.1 Parallel Lines and Transversals 3.2 Angles and Parallel Lines 3.5 Proving Lines Parallel 3.3 Slopes of Lines 3.4 Equations of Lines Segment Addition Postulate, Angle Addition Postulate Supplement Theorem, Complement Theorem, Vertical Angle Theorem, Right Angle Theorems parallel lines, parallel planes, skew lines, angles formed by transversals slope slope-intercept and point-slope form of equations of lines 9 October 4-8 *16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 3.6 Perpendiculars and Distance End of 1 st Quarter Review District Benchmark One 1.0, 2.0, 3.0, 4.0, 7.0, 16.0, 17.0 equidistant Department of Secondary Instruction Page 2 of 8 Updated 7/8/10

3 Glencoe Geometry Quarter 2 10 October October October Nov Nov Nov *12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. congruence and they are able to use the concept of corresponding parts of congruent triangles. congruence *12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. 6.0 Students know and are able to use the triangle inequality theorem. *3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. 6.0 Students know and are able to use the triangle inequality theorem. congruence and they are able to use the concept of corresponding parts of congruent triangles. *12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. 4.1 Classifying Triangles 4.2 Angles of Triangles Congruent Triangles 4.3 Congruent Triangles 4.4 Proving Congruence-SSS, SAS 4.5 Proving Congruence-ASA, AAS 4.6 Isosceles Triangles 4.7 Triangles and Coordinate Proof Triangle Relationships 5.1 Bisectors, Medians, and Altitudes 5.2 Inequalities and Triangles 5.4 The Triangle Inequality 5.4 The Triangle Inequality 5.3 Indirect Proof Site Based Common Assessment Algebra topics prerequisite for Chapter 6: Solve an equation by taking the square root. See Algebra I book sections 8-6. Quadrilaterals 6.1 Angles of Polygons 6.2 Parallelograms 6.3 Tests for Parallelograms Thanksgiving Break Classify s by sides & by s, Sum Theorem, 3 rd Thm, Exterior Thm Congruent Triangles, CPCTC, SSS, SAS, ASA, AAS, HL Isosceles Thm perpendicular bisector, concurrent lines, point of concurrency, median, altitude (height) circumcenter, incenter, centroid, orthocenter, Algebraic Properties of Inequality, Inequality Theorems in s Inequality Thm, Indirect Proof, Proof by Contradiction Interior & Exterior s of Polygons, Definition & Properties of Parallelogram Department of Secondary Instruction Page 3 of 8 Updated 7/8/10

4 Glencoe Geometry Quarter 2 16 Nov/Dec Dec congruence and they are able to use the concept of corresponding parts of congruent triangles. 6.4 Rectangles 6.5 Rhombi and Squares 6.6 Trapezoids 6.7 Coordinate Proof with Quadrilaterals Algebra topics prerequisite for Chapter 7: Proportions & Cross-products Simplify radical expressions See Algebra I book sections 2-6 & 10-3 End Semester Review Def. & Properties of Rectangle, Rhombus, Square, Trapezoid, Kite, Isosceles Trapezoid District Benchmark Two 2.0, 4.0, 5.0, 7.0, 12.0, Dec Final Exams Winter Break Department of Secondary Instruction Page 4 of 8 Updated 7/8/10

5 19 January January January Jan/Feb 31-4 FONTANA UNIFIED SCHOOL DISTRICT Glencoe Geometry Quarter 3 *2.0 Students write geometric proofs, including proofs by 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. *2.0 Students write geometric proofs, including proofs by *3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. 5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. properties of quadrilaterals, and the properties of circles. *12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. *12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. *14.0 Students prove the Pythagorean theorem Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles Students know and are able to use angle and side relationships in problems with special right triangles, such as 30, 60, and 90 triangles and 45, 45, and 90 triangles. *18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x)) 2 + (cos(x)) 2 =1 *19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side Students know and are able to use angle and side relationships in problems with special right triangles, such as 30, 60, and 90 triangles and 45, 45, and 90 triangles. Proportions & Similarity 7.1 Proportions 7.2 Similar Polygons 7.3 Similar Triangles 7.4 Parallel Lines and Proportional Parts 7.5 Parts of Similar Triangles Right Triangles & Trigonometry 8.1 Geometric Mean 8.2 The Pythagorean Theorem and Its Converse 8.3 Special Right Triangles 8.3 Special Right Triangles 8.4 Trigonometry 8.5 Angles of Elevation and Depression Site Based Common Assessment Algebra topics prerequisite for Chapter 10: Quadratic Formula Solving Quadratics by Factoring. See Algebra I book sections 8-3 & 9-4 Means Extremes Property, ratio, proportion, similar figures, scale factor, AA~, SSS~, SAS ~ Midsegment Thm Proportionality Thm geometric mean, Similar Rt s Pythagorean Triples rt. s rt. s sine, cosine, tangent ratios, angle of elevation, angle of depression Department of Secondary Instruction Page 5 of 8 Updated 7/8/10

6 FONTNA UNIFIED SCHOOL DISTRICT Glencoe Geometry Quarter 3 23 Feb Feb Feb Feb/Mar March March *21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. congruence and they are able to use the concept of corresponding parts of congruent triangles. *21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. congruence and they are able to use the concept of corresponding parts of congruent triangles. *21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. distance formula, and various forms of equations of lines 11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. *22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. Circles 10.1 Circles 10.2 Measuring Angles and Arcs 10.3 Arcs and Chords 10.4 Inscribed Angles 10.5 Tangents 10.6 Secants, Tangents, and Angle Measures 10.7 Special Segments in a Circle circle, center, name of circle, radius, diameter, chord, pi, central angle, arc measure, arc length, Chord & Arc Theorems, inscribed polygon, circumscribed circle inscribed angle, intercepted arc, Inscribed Thms, tangent lines, point of tangency, inscribed circle, circumscribed polygon s formed by chords, secants & tangents, proportional segments formed by chords, secants & tangents 10.8 Equations of Circles standard form for equation of circle Transformation 9.1 Reflections 9.2 Translations 9.3 Rotations CAHSEE District Benchmark Three 4.0, 8.0, 12.0, 15.0, 17.0, 19.0, 21.0, 22.0 transformation, translation, reflection, rotation, preimage, image, isometry, symmetry Department of Secondary Instruction Page 6 of 8 Updated 7/8/10

7 FONTNA UNIFIED SCHOOL DISTRICT Glencoe Geometry Quarter Mar-Apr April Apr 4- May 6 31 April April April May 2-6 Review for CST Testing 9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders. CST Testing Window *10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. *10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. *21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. 9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders. 9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders. Use Mastering the CA Mathematics Standards Workbook and textbook pages CA1-CA Three Dimensional Figures polyhedron, prism, pyramid, cylinder, cone, sphere, surface area, volume, face, edge, vertex Area of Polygons & Circles 11.1 Areas of Parallelograms 11.2 Areas of Triangles, Trapezoids, and Rhombi 11.3 Areas of Regular Polygons and Circles 11.4 Areas of Composite Figures 11.5 Geometric Probability and Areas of Sectors Surface Area & Volume 12.2 Surface Area of Prisms 12.3 Surface Area of Cylinders 13.1 Volumes of Prisms and Cylinders 12.4 Surface Area of Pyramids 12.5 Surface Area of Cones 13.2 Volumes of Pyramids and Cones apothem, regular polygon, sector characteristics of prism & cylinder, lateral faces, lateral edge, altitude, base, base edge, right & oblique solids, lateral area, base area, total surface area, volume characteristics of pyramid & cone, vertex, slant height Department of Secondary Instruction Page 7 of 8 Updated 7/8/10

8 Glencoe Geometry Quarter 4 35 May May May Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids Surface Area of Spheres 13.3 Volumes of Spheres 13.4 Congruent and Similar Solids End of Semester Review Final Exams, Final Wrap-Up characteristics of sphere, great circle, scale factor, side ratio a:b, perimeter ratio a:b, area ratio a 2 : b 2, volume ratio a 3 : b 3 Department of Secondary Instruction Page 8 of 8 Updated 7/8/10