GEOMETRY
COURSE OVERVIEW
COURSE GOAL: To increase mathematical skills and satisfy the requirements
for a high school geometry course.
COURSE OBJECTIVES: During the course, students
will demonstrate skills with the following:
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Basic definitions, use of postulates from algebra, angles
and special pairs of angles, postulates and theorems of geometry, inductive and
deductive reasoning, and writing formal geometric proofs in the two-column
format. Math EALR?s 1.1,
1.3, 3.1, 3.2, 3.34.1, 4.2, 4.3)
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Properties of parallel lines and planes, proving lines
are parallel, applying parallel lines to polygons, If-Then statements and their
converses, inverses, and contrapositives. (Math EALR?s 1.3, 2.1, 3.1, 3.2, 3.3,
4.2, 4.3)
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Congruence of triangles and polygons, proving triangles
are congruent, using congruent triangles, medians and altitudes of triangles,
and classifying triangles. (Math EALR?s
1.3, 3.1, 3.2, 3.3, 4.2, 4.3)
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Properties of parallelograms, special parallelograms,
proving quadrilaterals are parallelograms, properties of trapezoids, concurrent
lines and indirect proofs. (Math EALR?s
1.3, 2.1, 2.2, 2.3, 3.1, 3.3, 4.2, 4.3)
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Definitions and properties of ratio and proportion,
similar polygons, similarity theorems and sides divided proportionally. (Math EALR?s 1.1, 1.3, 1.5, 2.3, 3.1,
3.3, 4.2, 5.1, 5.3)
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Geometric means, using the Pythagorean Theorem to solve
right triangles, special right triangle theorems, using the sine, cosine and
tangent ratios to solve right triangles. (Math EALR?s 1.1, 1.2, 1.3, 1.5, 2.3, 3.1, 3.3, 4.2, 5.1, 5.2,
5.3)
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Definitions and basic terms for circles, tangents, arcs
and chords of circles, inscribed angles, and polygons inscribed in circles.
(Math EALR?s 1.3, 1.5, 3.1,
3.3, 4.2, 5.2, 5.3)
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Areas of rectangles, parallelograms, triangles,
trapezoids and regular polygons. Circumference and area of
circles, area of sectors and arc lengths of circles, and area of similar
figures. (Math EALR?s
1.1, 1.2, 1.3, 1.5, 2.2, 2.3, 5.1, 5.2, 5.3)
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Lateral area, total area and volume of geometric solids
including prisms, pyramids, cylinders, cones and spheres. Areas
and volumes of similar solids. (Math EALR?s 1.1, 1.2, 1.3, 1.5, 2.2, 2.3, 5.1, 5.2, 5.3)
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Coordinate geometry to include the distance and midpoint
formulas, slope of a line, parallel and perpendicular lines, and equations for
lines and circles. (Math EALR?s
1.1, 1.2, 1.3, 1.5, 2.3, )
MATERIALS: Geometry, New Edition, Jurgensen,
etal.
Teacher-made supplements and tests
Adapted materials for students with visual impairments
Students will be required to keep a geometry notebook containing
all definitions, theorems and postulates studied in class.
GRADING:
Attendance and daily work: 50%
Class participation: 10%
Geometry notebook: 10%
Tests: 30%
TIME LINE: Time lines are approximate and are dependent on the on the
readiness and abilities of the students. We will cover 10 chapters of the text,
spending 3-4 weeks on each chapter.
3-4 WEEKS: Chapter 1: Introduction to undefined terms and their use in
other definitions. Definition of angles, postulates from
algebra, special pairs of angles, beginning theorems, deductive reasoning and
proofs, postulates of points, lines and planes.
3-4 WEEKS: Chapter 2: Definitions and properties of parallel lines, proving
lines are parallel, angles of a triangle, angles of a polygon, If-Then
statements and their converses, inverses and contra positives.
3-4 WEEKS: Chapter 3: Definition of congruent figures, corresponding parts
in a congruence, ways to prove triangles congruent, using congruent triangles,
the isosceles triangle theorems, medians and altitudes of triangles,
overlapping triangles, using more than one pair of congruent triangles,
inductive reasoning.
3-4 WEEKS: Chapter 4: Properties of parallelograms, special parallelograms,
ways to prove that quadrilaterals are parallelograms, properties of trapezoids,
concurrent lines, indirect proofs, equalities for one and two triangles.
3-4 WEEKS: Chapter 5: Definition of ratio and proportion, properties of
proportions, similar polygons, AA Postulate, similarity theorems, sides of
polygons divided proportionally.
3-4 WEEKS: Chapter 6: Finding the geometric mean between two numbers, the
Pythagorean Theorem, converse of the Pythagorean Theorem, special right
triangle theorems, the tangent ratio, the sine and cosine ratios, using the
trigonometric ratios to solve problems.
3-4 WEEKS: Chapter 7: Definitions for tangents, arcs, and chords of
circles, relationships between arcs and central angles and between arcs and
chords, inscribed angles of a circle, inscribed polygons of a circle, other
angles related to circles, relationships between circles and lengths of
segments.
3-4WEEKS: Chapter 9: Formulas for the areas of rectangles, squares,
triangles, parallelograms, trapezoids, and regular polygons. Circumference
and area of circles, area of sectors of circles, arc lengths of sectors of
circles, areas of similar polygons.
3-4 WEEKS: Chapter 10: Surface areas and volumes of solids, including
prisms, pyramids, cylinders, cones, and spheres. Areas and
volumes of similar solids.
3-4WEEKS: Chapter 11: Coordinate geometry including the distance and
midpoint formulas, equations for circles, slope of lines, parallel and
perpendicular lines, and equations of lines.