COURSE OF STUDY OUTLINE
DEPARTMENT: MATHEMATICS
COURSE TITLE: Geometry
Grade Level: 9-12 Length: Two semesters Number of Credits: Ten Units Prerequisites: Earned a “C” or better in Algebra 1.
COURSE DESCRIPTION:
Geometry is the second year of three years of college-prep math required for entrance to a four year college or university. Geometry covers plane and solid geometry as well as coordinate geometry topics as they relate to both abstract math concepts and real-world situations. Topics include logic and proof, points, lines and planes, fundamental definitions and concepts, triangles, quadrilaterals, parallel lines, polygons, perimeter and area of polygons, surface area and volume of solids, circumference and area of circles, area and volume of spheres, similarity, congruence, trigonometry and analytic geometry. Students do deductive proofs, coordinate proofs and proof by contradiction and are introduced to inductive reasoning.
RATIONALE FOR THE COURSE:
Geometry requires students to think logically and sequentially. Critical thinking, reading comprehension, and independent learning are developed. Student must participate in discussion and are frequently engaged in discovery. Students will develop the thinking skills and receive the geometry concepts that will be needed for higher level math courses. Students will have more tools to approach problems of all types and to be more logical and effective in coming up with solutions.
This course meets an a-g UC/CSU requirement.
EXPECTED SCHOOL WIDE LEARNING RESULTS (ESLRS):
1. Informed 2. Excellent 3. Purposeful COURSE OUTLINE (Numbers in parentheses indicate CA Standard):
Chapter 1: Points, Lines and Planes. Points, lines and planes. Linear measure and precision. Distnace and midpoints. Angle measure. Angle relationships. Polygons. ( 1.0, 8.0. 11.0, 15.0, 16.0 )
Chapter 2: Reasoning and Proof Inductive reasoning and conjecture. Logic. Conditional statements. Deductive reasoning. Postulates and paragraph proofs. Algebraic proofs. Proving segment relationships. Proving angle relationships. ( 1.0, 2.0, 3.0, 4.0)
Chapter 3: Parallel and Perpendicular Lines Parallel lines and transversals. Angles and parallel lines. Slopes of lines. Equations of lines. Proving lines parallel. Perpendiculars and distance. . (1.0, 2.0, 6.0, 7.0, 16.0, 17.0)
Chapter 4: Congruent Triangles Classifying triangles. Angles of triangles. Congruent triangles. Proving congruence (SSS, SAS, ASA, AAS). Isosceles triangles. Triangles and coordinate proofs. ( 4.0, 5.0 )
Chapter 5: Relationships in Triangles Bisectors, medians, and altitudes. Inequalities and triangles. Indirect proof. The triangle inequality. ( 5.0, 6.0 )
Chapter 6: Proportions and Similarity Proportions. Similar polygons. Similar triangles. Parallel lines and proportional parts. Parts of similar triangles. ( 5.0)
Chapter 7: Right Triangles and Trigonometry Geometric mean. The Pythagorean thm and its converse. Special right triangles. Trigonometry. Angles of elevation and depression. The law of sines. ( 2.0, 18.0, 19.0, 20.0)
2 Chapter 8: Quadrilaterals Angles of polygons. Parallelograms. Test for parallelograms. Rectangles. Rhombi and squares. Trapezoids. Coordinate proofs with quadrilaterals. ( 2.0, 3.0, 4.0, 7.0,12.0, 16.0, 17.0)
Chapter 9: Transformations Reflections. Translations. Rotations. (22.0)
Chapter 10: Circles Cirlces and circumference. Angles and arcs. Arcs and chords. Inscribed angles. Tangents. Secants, tangents and angle measure. Special segments in a circle. Equations of circles. (2.0, 7.0, 16.0, 21.0) Chapter 11: Areas of Polygons and Circles Areas of parallelograms, triangles, trapezoids, rhombi, regular polygons and cirlces. Area of irregular figures. Geometric probability (8.0, 10.0, 11.0)
Chapter 12: Surface Area Three dimensional figures. Nets and surface area. Surface area of prisms, cylinders, pyramids, cones and spheres. (8.0, 9.0)
Chapter 13: Volume Volume of prisms, cylinders, pyramids, cones and spheres. Congruent and similar solids. Coordinates in space. (8.0, 9.0, 11.0, 20.0)
SUGGESTED TEACHING STRATEGIES
I. Lecture II. Cooperative learning groups III. Lab investigations IV. Student explanations and presentations V. Modeling VI. Peer tutoring
ASSESSMENTS
I. Oral questions/answers II. Written quizzes and examinations
3 III. Portfolio assignments IV. Pre- and post- tests V. Growth-over-time problems
RESOURCES
Textbooks: Geometry-California Edition, McGraw-Hill Glencoe
Geometry
Grades Eight Through Twelve - Mathematics Content Standards
The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems.
1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
2.0 Students write geometric proofs, including proofs by contradiction.
3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.
4.0 Students prove basic theorems involving congruence and similarity.
5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.
6.0 Students know and are able to use the triangle inequality theorem.
7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.
8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
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.
10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
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.
13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.
14.0 Students prove the Pythagorean theorem.
4 15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
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.
17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.
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.
20.0 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.
21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.
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