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Maui Community College
Course Outline
1. Alpha and Number:
Math 35
Course Title:
Geometry
Number of Credits:
3
Date of Course Outline:
March 22, 2004
2. Course Description:
Studies Euclidean space including the
topics of parallelism, congruence,
deductive reasoning, similarity, circles
and measurement.
3. Contact Hours/Type:
3 Hour/Lecture
4. Prerequisites:
Math 25 with at least a C or Placement
at Math 27 and English 22 with at least
a C or placement at English 100, or
consent.
Corequisites:
Recommended Preparation:
At least 11th grade reading skills
Approved by: ___________________________
__
Date: _________________
Math 35 – Course Outline – March 22, 2004
page 2
5. General Course Objectives: Prepares student for sequence of math courses which
lead to calculus. Teaches basic geometric terms, symbols of geometry, drawing
diagrams, charts and figures, how to interpret and write simple proofs, and
applications of basic definitions, postulates and theorems.
6. Specific Course Competencies: Upon the successful completion of this course the
student will be able to:
a. Understand the terms point, line, and plane and draw representations of them
b. Use undefined terms to define some basic terms in geometry
c. Use symbols for lines, segments, rays, and distances; find distances
d. Name angles and their measures
e. Use properties from algebra and the first geometric postulates in two-column
proofs
f.
Know various kinds of reasons used in proofs
g. Apply the definitions of complementary, supplementary, and vertical angles
h. Apply the Midpoint Theorem, the Angle Bisector Theorem, and the theorem
about vertical angles
i.
State and apply the theorems about perpendicular lines, supplementary angles,
and complementary angles
j.
Recognize the information conveyed by a diagram
k. Plan and write two-column proofs
l.
Understand the relationships described in the postulates and theorems
relating points, lines, and planes
m. Distinguish between intersecting lines, parallel lines, and skew lines
n. State and apply the theorem about the intersection of two parallel planes by a
third plane
o. Identify the angles formed when two lines are cut by a transversal
p. State and apply the postulates and theorems about parallel lines
Math 35 – Course Outline – March 22, 2004
page 3
q. State and apply the theorems about a parallel and a perpendicular to a given line
through a point outside the line
r. Classify triangles according to sides and to angles
s. State and apply the theorem and the corollaries about the sum of the measures
of the angles of a triangle
t. State and apply the theorem about the measure of an exterior angle of a triangle
u. Recognize and name convex polygons and regular polygons
v. Find the measures of interior angles and exterior angles of convex polygons
w. Identify the corresponding parts of congruent figures
x. Use the SSS Postulate, the SAS Postulate, and the ASA Postulate to prove two
triangles congruent
y. Deduce information about segments or angles by first proving that two triangles
are congruent
z. Apply the theorems and corollaries about isosceles triangles
aa. Use the AAS Theorem to prove two triangles congruent
bb. Use the HL Theorem to prove two right triangles congruent
cc. Prove that two overlapping triangles are congruent
dd. Apply the definitions of the median and the altitude of a triangle and the
perpendicular bisector of a segment
ee. State and apply the theorem about a point on the perpendicular bisector of a
segment, and the converse
ff. Apply the definitions of a parallelogram and a trapezoid
gg. State and apply the theorems about properties of a parallelogram
hh. Prove that certain quadrilaterals are parallelograms
ii. Identify the special properties of a rectangle, a rhombus, and a square
jj. State and apply the theorems about the median of a trapezoid and the segment
that joins the midpoints of two sides of a triangle
Math 35 – Course Outline – March 22, 2004
page 4
kk. Express a ratio in simplest form
ll.
Solve for an unknown term in a given proportion
mm. Express a given proportion in an equivalent form
nn. State and apply the properties of similar polygons
oo. Use the AA Similarity Postulate, the SAS Similarity Theorem, and the SSS
Similarity Theorem to prove that two triangles are similar
pp. Deduce information about segments or angles by first proving that two
triangles are similar
qq. Apply the Triangle Proportionality Theorem and its corollary
rr.
State and apply the Triangle Angle-Bisector Theorem
ss. Determine the geometric mean between two numbers
tt.
State and apply the relationships that exist when the altitude is drawn to the
hypotenuse of a right triangle
uu. State and apply the Pythagorean Theorem
vv. State and apply the converse of the Pythagorean Theorem and related
theorems about obtuse and acute triangles
ww. Determine the lengths of two sides of a 45°, 45°, 90° triangle or a
30°, 60°, 90° triangle when the length of the third side is known
xx. Define a circle, a sphere, and terms related to them
yy. Recognize circumscribed and inscribed polygons and circles
zz. Apply theorems that relate tangents and radii
aaa. Define and apply properties of arcs and central angles
bbb. Apply theorems about the chords of a circle
ccc. Solve problems and prove statements involving inscribed angles
ddd. Solve problems and prove statements involving angles formed by chords,
secants, and tangents
Math 35 – Course Outline – March 22, 2004
page 5
eee. Solve problems involving lengths of chords, secant segments, and tangent
segments
fff.
Define the area of a polygon
ggg. State the area postulates
hhh. State and use the formulas for the areas of rectangles, parallelograms,
triangles, and trapezoids
iii.
State how the area and perimeter formulas for regular polygons relate to the
area and circumference formulas for circles
jjj.
Compute the circumferences and areas of circles
kkk.
Compute arc lengths and the areas of sectors of a circle
lll.
Apply the relationships between scale factors, perimeters, and areas of
similar figures
mmm. Identify the parts of prisms, pyramids, cylinders, and cones
nnn.
Find the lateral area, total area, and volume of a right prism or regular
pyramid
ooo.
Find the lateral area, total area, and volume of a right cylinder or cone
ppp.
Find the area and the volume of a sphere
qqq.
State and apply the properties of similar solids
7. Recommended course content and approximate time spent
Linked to #6. Student Learning Outcomes.
A. Points, lines, planes, and Angles - 3 weeks
a) Undefined terms and basic definitions
i) Points, lines, and planes (6a, 6b)
ii) Segments, Rays, and Distance (6b, 6c)
iii) Angles (6d)
b) Introduction to Proof
i) Properties from Algebra (6e)
ii) Proving theorems (6f, 6h)
iii) Special Pairs of Angles (6g, 6h, 6i)
c) More about Proof
i) Perpendicular lines (6i)
ii) Planning a Proof (6j, 6k)
iii) Postulates Relating Points, Lines, and Planes (6l)
Math 35 – Course Outline – March 22, 2004
page 6
B. Parallel Lines and Planes - 2 weeks
a) When lines and planes are parallel
i) Definitions (6m, 6n, 6o)
ii) Properties of Parallel lines (6p, 6q)
iii) Proving lines parallel (6p)
b) Applying parallel lines to polygons
i) Angles of a triangle (6r, 6s, 6t)
ii) Angles of a polygon (6u, 6v)
C. Congruent Triangles - 2 weeks
a) Corresponding Parts in a Congruence
i) Congruent figures (6w)
ii) Some ways to prove triangles congruent (6x)
iii) Using congruent triangles (6y)
b) Some theorems based on congruent triangles
i) The isosceles triangle theorems (6z)
ii) Other methods of proving triangles congruent (6aa, 6bb, 6cc)
c) More about proof in geometry
i) Medians, Altitudes, and perpendicular bisectors (6dd, 6ee)
D. Using Congruent Triangles - 1 week
a) Parallelograms and Trapezoids
i) Properties of Parallelograms (6ff, 6gg))
ii) Ways to prove that quadrilaterals are parallelograms (6hh)
iii) Special parallelograms (6ii)
iv) Medians of Trapezoids and the segment joining the midpoints
of two sides of a triangle (6jj)
E. Similar Polygons - 1 week
a) Ratio, proportion, and similarity
i) Ratio and proportion (6kk)
ii) Properties of proportions (6ll, 6mm)
iii) Similar polygons (6nn)
b) Working with Similar Triangles
i) A postulate for similar triangles (6oo, 6pp)
ii) Theorems for similar triangles (6oo, 6pp)
iii) Proportional lengths (6qq, 6rr)
F. Right Triangles - 1 week
a) The Pythagorean Theorem
i) Geometric means (6ss, 6tt)
ii) The Pythagorean Theorem (6uu)
b) Right triangles
i) The converse of the Pythagorean Theorem (6vv)
ii) Special Right Triangles (6ww)
Math 35 – Course Outline – March 22, 2004
page 7
G. Circles - 2 weeks
a) Tangents, Arcs, and chords
i) Basic terms (6xx, 6yy)
ii) Tangents (6zz)
iii) Arcs and central angles (6aaa)
iv) Arcs and chords (6bbb)
b) Angles and segments
i) Inscribed angles (6ccc)
ii) Other Angles (6ddd)
iii) Circles and lengths of segments (6eee)
H. Areas of plane figures - 1 1/2 weeks
a) Areas of polygons
i) Areas of rectangles (6fff, 6ggg, 6hhh)
ii) Areas of parallelograms and triangles (6hhh)
iii) Areas of trapezoids (6hhh)
b) Circles and Similar Figures
i) Circumference and area of a circle (6iii, 6jjj)
ii) Areas of sectors and arc lengths (6kkk)
iii) Areas of similar figures (6lll)
I. Areas and Volumes of Solids - 1 1/2 weeks
a) Important Solids
i) Prisms (6mmm, 6nnn)
ii) Pyramids (6mmm, 6nnn)
iii) Cylinders and cones (6ooo)
b) Areas and volumes of similar solids (6ppp, 6qqq)
8. Recommended course requirements: Regularly assigned homework and in-class
assignments, regular quizzes, unit exams, and a final exam.
9. Text and materials: An appropriate text(s) and materials will be chosen at the
time the course is to be offered from those currently available in the field.
Examples include:
Geometry by Jurgensen, Ray C., Brown, Richard G., and Jurgensen, John W.;
Houghton Mifflin Company; Boston, Mass., 1988
10. Evaluation and grading:
A student's grade in the course is determined by computing an average of the
semester's course work which would include quizzes (40 –50%) , unit
exams (30 – 40%), and a final exam (10 – 30%) . It is not appropriate to evaluate
a student’s competency in a mathematics course by using only a mid-term and a
final exam. The homework may be included in the final grade (0% - 5%)
Math 35 – Course Outline – March 22, 2004
page 8
In the math department, grades are usually assigned according to the following
scale:
A: 90% - 100%
B: 80% - 89%
C: 70% - 79%
D: 60% - 69%
N or F: 0% - 59%
A student may select the option to receive a “credit/no credit” for the course
instead of a letter grade. If he/she wishes to select this option, he/she must
inform the instructor.
Some flexibility is given to instructors in these matters. Each instructor will
clearly inform students on his/her syllabus what the forthcoming course work
will entail and how it will be weighted and graded respectively.
11. Methods of Instruction: This course is usually taught in an individualized
study format in a math lab. Students are given instructor-prepared handouts
detailing sections to read and assignments to do, along with instructions on when
to take quizzes and exams. Lots of problems are assigned for each topic with each
student checking his/her own work. Students work for short period of time one-onone with an instructor or tutor. The student would be expected to learn more on
his/her own by reading the textbook. Frequent quizzes and/or exams are used to
monitor and inform students of their progress.