Lecture Twenty One
Surface Areas
May 2, 2007
Surface Area of Right Prisms
See example 11-18, page 788
Surface Area of a Cylinder
Surface Area of a Pyramid
See example 11-19, page 790; example 11-20, page 790
Surface Area of a Cone
S.A. = r2 + rl
Example 1
Lecture Nine
Polygons
February 21, 2007
A simple curve does not cross itself. A closed curve can be drawn starting
and stopping at the same point. Polygons are simple and closed and have
sides that are segments. A point where two sides of a polygon meet i
Lecture Eight
Basic Notations
February 22, 2007
The fundamental building blocks of geometry are points, lines and planes.
The building blocks are undened terms in order to avoid circular denitions.
See how to express three concepts by letters on page 573.
Lecture Seven
Measure of Central Tendency and Variation
February 14, 2007
Two Important aspects of data are its center and its spread
Measures of central tendency that describe where data are centered.
Mean
The arithmetic mean of the numbers x1, x2, , xn,
Lecture Six
Statistical Graphs
February 13, 2007
Two types of data
Numerical Data: Height, weight with measure units of length, pound, respectively.
Categorical Data: Such as blood type, hair color.
Numerical data can be described by a table and following
Lecture Five
Using Permutations and Combinations in Probability
February 7, 2007
Permutations of Unlike Objects
An arrangement of things in a denite order with no repetitions is a permutation.
Example
Given four dierent colors of balls cfw_R, Y, G, B in
Lecture Four
Odds, Conditional Probability, and Expected Value
January 31, 2007
Denition of Odds
Let P (A) be the probability that A occurs and P (A) be the probability that
A does not occur. Then the odds in favor of an event A are
P (A)
P (A)
,
1P (A) ,
Lecture Three
Using Simulations in Probability
January 29, 2007
A simulation is a technique used to act out a problem by conducting experiments whose outcomes are analogous to the original problem.
Example One
Simulate the results of ipping a coin 100 tim
Lecture Two
Tree Diagrams
January 24, 2007
Property: Multiplication Rule of Probabilities for Tree Diagrams
For all multistage experiments, the probability of the outcome along any
path of a tree diagram is equal to the product of all the probabilities al
Lecture Ten
More about Angles
February 28, 2007
Vertical angles are pairs of angles such 1 and 3 on gure 9-20 on page
600. Any line that intersects a pair of lines is a transversal of those lines.
In gure 9-21, line p is a transversal of lines m and n.
Su
Lecture Eleven
Geometry in Three Dimensions
March 5, 2007
Simple Closed Surfaces
A simple closed surface has exactly one interior, has not holes, and
is hollow.
A sphere is dened as the set of all points at a given distance from a given
point, the center.
Lecture Twelve
Congruence Through Constructions
March 15, 2007
In mathematics, similar ( ) objects have the same shape but not necessarily the same size, congruent ( objects have the same size as well as
=)
the same shape.
Denition of Congruent Segments a
Lecture Twenty
The Pythagorean Theorem and the distance Formula
April 19, 2007
Theorem 11-1, Pythagorean Theorem
If a right triangle has legs of lengths a and b and hypotenuse of length c,
then c2 = a2 + b2.
See Figure 11-39 for the proof.
Example 11-12,
Lecture Nineteen
Areas of Polygons and Circles
April 19, 2007
Areas on a Geoboard.
Example 11-6, page 751
Converting Units of Area
Unit
square kilometer
*square hectometer
*square dekameter
square meter
*square decimeter
square centimeter
square millimete
Lecture Eighteen
Linear Measure
April 19, 2007
The English System.
Unit Equivalent in Other Units
yard(yd)
3ft
foot(ft)
12in.
mile(mi)
1760 yd, or 5280 ft
Dimensional Analysis (Unit Analysis)
To convert from one unit of measure to another, the process kno
Lecture Seventeen
Lines in a Cartesian Coordinate System
April 19, 2007
A Cartesian coordinate system is constructed by placing two number lines
perpendicular to each other, as shown in Figure 10-74, page 707. The intersection point of the two lines is th
Lecture Fifteen
Similar Triangles and Similar Figures
April 9, 2007
Two gures that have the same shape but not necessarily the same size are
similar
Denition of Similar Triangles
ABC is similar to DEF , written ABC DEF , if, and only if,
AB
AC
A = D, B =
Lecture Sixteen
Trigonometry Ratios via Similarity
April 19, 2007
Two Observations
In two similar right triangles, the ration of one side to another in one triangle
will be the same as the ratio of the corresponding sides in the second triangle.
Specicall
Lecture Fourteen
Other Constructions
April 3, 2007
Constructing Parallel Lines
1.
2.
3.
4.
Rhombus Method, gure 10-26, page 670
Corresponding Angle Method, gure 10-27, page 670
By Using A Ruler and A Triangle, gure 10-28, page 671
Paper Folding, gure 10-2
Lecture Thirteen
Other Congruence Preperties
March 19, 2007
Angle, Side, Angle (ASA)
Property
Angle, Side, Angle (ASA) If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle,
respectively,
Lecture One How Probabilities Are Determined January 21, 2007 An experiment is an activity whose results can be observed and recorded. Each of the possible results of an experiment is an outcome. A set of all possible outcomes for an experiment is a sampl