# 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:

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

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

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)

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

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.