Maui Community College Course Outline 1. Alpha and Number: Math 35 Course Title: Geometry

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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 proo
fs, 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 fro
m 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, th
e 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 line
s, 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 theorem
s 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 lin
e



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 measu
re 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 congr
uent 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 th
e 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 definiti
ons 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 paral
lelogram 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 th
e 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 a
nd 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 Pythag
orean 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,


sec
ants, 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 polygon
s 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


p
yramid




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) Postula
tes 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) C
orresponding 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) Th
eorems 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 o
f 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) T
angents (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 v
olumes 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. Evaluati
on 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 appropri
ate 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 re
ceive 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
-
on
-


one with an instructor or tutor. The student would be expected to learn more on


his/her own by reading the textbook. Freq
uent quizzes and/or exams are used to


monitor and inform students of their progress.