Our Faculty Nicki Rosa BS, Mathematics MS, Computer Science Teaching Experience: Head of Math Department, Community Prep School, Colorado Springs, CO Founder, TotalMath.net Michael Hosking B.S., Biology; Ph.D., Ecology, Evolution and Organismal Biology Teaching experience: Davidson College (Davidson, NC) Gary Schwartz M.S., Ph.D., Mathematics Teaching experience: University of Oklahoma, Northern Illinois University Castle Rock

Lecture Hall - Current and Upcoming Lectures ARCHIVED LECTURES Date: Time: Length: 2002.7.15 11:30 PM PST 15 min. Introduction to PersonalProfessors — Please view before beginning your studies! MORE DETAILS… Date: Time: Length: 2003.9.11 12:15 PM PST 15 min. Geometric Terms & Notations — What is a plane, a point and a line? To get us off to a good start, we must first understand several geometric terms and get acquainted with their notations. MORE DETAILS… Date: Time: Length: 2003.9.16 12:15 PM PST 15 min. Geometric Terms & Notations Continued — We will continue where we left off with the previous lecture. Next up ... angles! MORE DETAILS… Date: Time: Length: 2003.9.18 12:15 PM PST 15 min. Geometric Postulates & Theorems — We will discover the differences and similarities between math rules & properties, postulates and theorems. MORE DETAILS… Date: Time: Length: 2003.9.23 12:15 PM PST 15 min. Similar, Congruent & More — What is the difference between similar and congruent? And more things to know: like midpoint and perpendicular and ... MORE DETAILS… Date: Time: Length: 2003.9.25 12:15 PM PST 15 min. Point, Line & Plane Postulates — These are an important foundation for all of our studies in geometry. MORE DETAILS… Date: Time: Length: 2003.9.30 12:15 PM PST 15 min. Properties of Equality & Congruence — In this lecture we cover eight properties of equality and three properties of congruence ... MORE DETAILS… Date: Time: Length: 2003.10.2 12:15 PM PST 20 min. Special Pairs of Angles — We will define four special pairs of angles. MORE DETAILS… Date: Time: Length: 2003.10.7 12:15 PM PST 15 min. Exploring Lines and Planes — Let's study relationships between two lines: parallel, intersecting and oblique. We will also continue to explore perpendicular lines and planes. MORE DETAILS… Date: Time: Length: 2003.10.9 12:15 PM PST 45 min. Geometric Connections to Algebra — In algebra, you learned that a system of two linear equations in x and y can have exactly one solution, no solution, or infinitely many solutions. Geometrically, this means that their graphs can be intersecting lines, parallel lines, or the same line. MORE DETAILS… Date: Time: Length: 2003.10.14 12:15 PM PST 20 min. Connections to Algebra Part 2 — We will continue our lesson that reviews our algebra skills. This part covers equations of parallel and perpendicular lines. MORE DETAILS… Date: Time: Length: 2003.10.16 12:15 PM PST 20 min. Using the Laws of Logic — Let's talk about conditional statments having hypotheses and conclusions. Then we will use the laws of logic to reason. MORE DETAILS… Date: Time: Length: 2003.10.21 12:15 PM PST 20 min. Styles of Proofs - The Paragraph Proof — A paragraph proof is written as a narrative. It explains the reasoning that a person might use to convince herself or himself that the statement is true. MORE DETAILS… Date: Time: Length: 2003.10.23 12:15 PM PST 15 min. Styles of Proofs - The Flow Proof — A flow proof uses arrows to show the flow of the logical argument. A reason is written below each statement. MORE DETAILS… Date: Time: Length: 2003.10.28 12:15 PM PST 15 min. Styles of Proofs - The Two-Column Proof — A two-column proof is a sequence of statements and a justification or 'reason' in a column next to it. Each statement is numbered to imply the logical order. MORE DETAILS… Date: Time: Length: 2003.10.30 12:15 PM PST 20 min. Angles Formed by a Transversal — A transversal is a line that intersects two or more coplanar lines at different points. This creates several different types of angles which we'll examine in this lesson. MORE DETAILS… Date: Time: Length: 2003.11.6 12:15 PM PST 20 min. Applications: Proof of Thm. 3.6 — A two-column proof of a new theorem (3.6) MORE DETAILS… Date: Time: Length: 2003.11.13 12:15 PM PST 15 min. Proving Lines are Parallel — When we used the postulates and theorems for transversal applications we KNEW the lines were parallel. Here we will apply the reverse .... MORE DETAILS… Date: Time: Length: 2003.11.14 12:15 PM PST 17 min. Using Properties of Parallel Lines — Transversals through a set of parallel lines create some interesting angles. MORE DETAILS… Date: Time: Length: 2003.11.18 12:15 PM PST 20 min. All About Triangles — Today we start learning about triangles. We will define the definition of congruent triangles as well as cover all the notation involved. Then ... MORE DETAILS… Date: Time: Length: 2003.11.20 12:15 PM PST 15 min. Angles of a Triangle — The word "triangle" means "three angles" of course. When the sides of a triangle are extended, however, other angles are formed. MORE DETAILS… Date: Time: Length: 2003.11.25 12:15 PM PST 15 min. Proving Triangles are Congruent — Congruence Postulates 17 and 18 as well as Postulate 19 and Theorem 4.7. These are all ways to prove triangles are congruent. MORE DETAILS… Date: Time: Length: 2003.12.2 12:15 PM PST 23 min. Using Congruent Triangles — What does CPCTC stand for? Well, we will use it when planning our next proof ... MORE DETAILS… Date: Time: Length: 2003.12.4 12:15 PM PST 22 min. Isosceles & Right Triangles — Properties of Isosceles Triangles includes Theorems 4.8 - 4.10 and their corollaries. Theorem 4.10 uses properties of right triangles. MORE DETAILS… Date: Time: Length: 2004.1.6 12:15 PM PST 15 min. Triangle Parts — More stuff on triangles! We will introduce theorems 5.1 - 5.4. They cover what the perpendicular bisector and angle bisector are. MORE DETAILS… Date: Time: Length: 2004.1.8 12:15 PM PST 20 min. Special Segments in a Triangle — They are: perpendicular bisector, angle bisector, median and altitude. We will also learn .... MORE DETAILS… Date: Time: Length: 2004.1.13 12:15 PM PST 15 min. The Midsegment Theorem — Another special segment of a triangle! It connects the midpoints of two sides of a triangle. What?!??!?! MORE DETAILS… Date: Time: Length: 2004.1.15 12:15 PM PST 15 min. Inequalities - One Triangle — In this lecture we will learn several triangle inequality theorems. MORE DETAILS… Date: Time: Length: 2004.1.20 12:16 PM PST 15 min. Inequalities in Two Triangles — Up to this point, all the proofs and problems we have worked have been DIRECT. That is, we have used rules and theorems to obtain direct conclusions. In this lesson, we will use INDIRECT proof ... MORE DETAILS… Date: Time: Length: 2004.1.22 12:15 PM PST 20 min. Polygons — On to a NEW "chapter"! What exactly is a polygon? How many sides does a heptagon have? What do I mean by "n-gon"? The answers to all these and more .... MORE DETAILS… Date: Time: Length: 2004.1.27 12:15 PM PST 15 min. Polygon Angles — We have already learned that the sum of the angles of a triangle are 180 degrees. We will use this property to find the sum of the interior angles of a convex polygon. MORE DETAILS… Date: Time: Length: 2004.1.29 12:15 PM PST 15 min. Parallelograms — What is one of these things? Using a ton of old vocabulary ... we will learn this and several other properties to go along. You will want to pay close attention because ... MORE DETAILS… Date: Time: Length: 2004.2.3 12:15 PM PST 15 min. Quadrilaterals ARE Parallelograms — Theorems 6.7 through 6.10 gives us a variety of ways to prove that a quadrilateral is a parallelogram. MORE DETAILS… Date: Time: Length: 2004.2.5 12:15 PM PST 15 min. Special Parallelograms — A rhombus, a square and a rectangle! Theorems 6.12 - 6.14 ... and a few more notes ... then .... MORE DETAILS… Date: Time: Length: 2004.2.10 12:15 PM PST 15 min. Trapezoids — Introduce Theorems 6.17 - 6.20 which will help us learn HOW to identify trapezoids and isosceles trapezoids ... MORE DETAILS… Date: Time: Length: 2004.2.12 12:15 PM PST 10 min. Kites — Well, unfortunately, we can't all go fly one together. We can, however, learn some properties about them. Who knew a simple childhood (and adult) activity involved geometry! MORE DETAILS… Date: Time: Length: 2004.2.17 12:15 PM PST 15 min. Rigid Motion — How to identify the three basic rigid transformations in a plane. These three are: reflection, rotation and translation. MORE DETAILS… Date: Time: Length: 2004.2.19 12:15 PM PST 18 min. Reflections — A reflection is an isometry. Example 1 will show finding a minimum distance ... MORE DETAILS… Date: Time: Length: 2004.2.24 12:15 PM PST 15 min. Rotations — A rotation is an isometry! Let's learn how to first recognize them and then ... MORE DETAILS… Date: Time: Length: 2004.2.26 12:15 PM PST 15 min. Translations — A translation is an isometry! Let's construct a few and then ... MORE DETAILS… Date: Time: Length: 2004.3.2 12:15 PM PST 15 min. Ratio & Proportion — How to compute the ratio of two numbers and how to solve problems using proportions. MORE DETAILS… Date: Time: Length: 2004.3.4 12:15 PM PST 15 min. Solving Proportions — How to use properties of proportions and how to use a problem solving plan for problems that can be solved by proportions. MORE DETAILS… Date: Time: Length: 2004.3.9 12:15 PM PST 13 min. Similar Polygons — How to identify similar polygons & how to use them to solve problems. MORE DETAILS… Date: Time: Length: 2004.3.11 12:15 PM PST 15 min. Similar Triangles — How to identify similar triangles and how to use them in coordinate geometry. MORE DETAILS… Date: Time: Length: 2004.3.16 12:15 PM PST 15 min. Proportions in Similar Triangles — Introducing theorems 8.4 - 8.7 and a bunch of examples! We will learn how to use these theorems to solve problems in geometry. MORE DETAILS… Date: Time: Length: 2004.3.18 12:15 PM PST 15 min. Proportions & Triangles Part 2 — Continuing the previous lecture .... MORE DETAILS… Date: Time: Length: 2004.3.30 12:15 PM PST 15 min. Right Triangles — As TERM 3 begins, we will start with everything you needed to know about Right Triangles. MORE DETAILS… Date: Time: Length: 2004.4.1 12:15 PM PST 15 min. The Altitude — The altitude has an attitude! (April Fools!) Let's talk about theorems 9.2 & 9.3 (both about the altitude. MORE DETAILS… Date: Time: Length: 2004.4.6 12:15 PM PST 12 min. Pythagorean Theorem & Triples — We will define the Pythagorean Theorem (hopefully again for most of you) and learn what a Pythagorean Triple is. MORE DETAILS… Date: Time: Length: 2004.4.8 12:15 PM PST 15 min. Classify Triangles — Remember back a few sections ago when we classified angles and basic triangles? That is what we are going to do this time ... just with RIGHT triangle knowledge! MORE DETAILS… Date: Time: Length: 2004.4.13 12:15 PM PST 9 min. 45-45-90 Triangles — Also known as the Isosceles Right Triangle, we will learn some important FACTS about the sides of it! MORE DETAILS… Date: Time: Length: 2004.4.15 12:15 PM PST 15 min. 30-60-90 Triangle — This famous triangle has some important facts as well. Brush up on your square roots before this lecture. MORE DETAILS… Date: Time: Length: 2004.4.20 12:15 PM PST 15 min. Trigonometric Ratios — Trigonometry means the measurement of triangles! We will learn what a trig ratio is and the definition of the 3 bsic ones. MORE DETAILS… Date: Time: Length: 2004.4.22 12:15 PM PST 25 min. Solving Right Triangles — In order to solve a right triangle you must have one of the following pieces of information: two side lengths, one side and one acute angle, OR one side and one trig ratio. MORE DETAILS… Date: Time: Length: 2004.4.27 12:15 PM PST 15 min. Circles — We will draw and indentify all the parts of a circle. MORE DETAILS… Date: Time: Length: 2004.4.29 12:15 PM PST 15 min. Tangents — We will continue our circle notes with drawings of several different types of tangents. MORE DETAILS… Date: Time: Length: 2004.5.4 12:15 PM PST 15 min. Properties of Tangents Continued — We will continue to apply our new learned properties of tangents to specific situations. Bring your notes from the previous lecture with you! MORE DETAILS… Date: Time: Length: 2004.5.6 12:15 PM PST 15 min. Ins & Outs — Introduction of what an inscribed and circumscribed circle are, complete with definitions and Mrs. G drawings! An example at the end of the lecture will serve as a mid-section review from what we have learned thus far about circles & their "parts". MORE DETAILS… Date: Time: Length: 2004.5.11 12:15 PM PST 15 min. Central Angles & Arcs — Learning how to measure central angles and arcs of circles. We have the Arc Addition Postulate to discuss and a few problems to apply this new information to. MORE DETAILS… Date: Time: Length: 2004.5.13 12:15 PM PST 15 min. Arcs & Chords — How to use properties of chords and arcs to solve problems. Definitions of four more theorems with, of course, drawings! MORE DETAILS… Date: Time: Length: 2004.5.18 12:15 PM PST 20 min. More About Circles — There are so many theorems on circles and their parts, I really didn't know what to name this lecture. So on with "more about circles"! MORE DETAILS… Date: Time: Length: 2004.5.20 12:15 PM PST 15 min. Circle Examples — Finally! All those theorems we have been defining have examples to go with them. Today, would like to work through five examples with you! They are different from each other and will show you just how many things we have learned about circles. GO TO THE ASSESSMENT CENTER AND PRINT OUT THE TEMPLATES FOR TODAY'S EXAMPLES! MORE DETAILS… Date: Time: Length: 2004.5.25 12:15 PM PST 15 min. Perimeter, Circumference & Arc Length — Definitions of the perimeter, circumference and arc length, complete with formulas for finding all. Examples for all as well! MORE DETAILS… Date: Time: Length: 2004.5.27 12:15 PM PST 15 min. AREA — How to find the AREA of just about EVERYTHING! A ton of formulas! A ton of examples! MORE DETAILS… Date: Time: Length: 2004.6.1 12:15 PM PST 15 min. Polyhedrons — Today we will learn about solids called polyhedrons. We'll talk about their faces, vertices and edges and more. MORE DETAILS… Date: Time: Length: 2004.6.3 12:15 PM PST 15 min. Surface Area of Prisms & Pyramids — The surface area means to add up the area of all the faces of the solid. For a prism and a pyramid we have two formulas to introduce. MORE DETAILS… Date: Time: Length: 2004.6.8 12:15 PM PST 15 min. Surface Area of Cones & Cylinders — Two new formulas. We will work not just a simple surface area example but ... MORE DETAILS… Date: Time: Length: 2004.6.10 12:15 PM PST 15 min. Volume — Boy do I have a list of volume formulas for you! A cube, a prism, a cylinder, a pyramid and a cone! All in one day! Piece of cake! Then I have three great examples for you! MORE DETAILS… Date: Time: Length: 2006.1.9 5:30 PM PST 18 min. Ratios of Perimeter, Area and Volume — In this lecture we will explore the ratios of perimeter, area and volumes of common geometric figures and solids. MORE DETAILS… Date: Time: Length: 2006.1.9 7:30 PM PST 12 min. Basic Constructions — We will learn how to do basic constructions using a compass and a straightedge MORE DETAILS… Date: Time: Length: 2006.1.9 8:30 PM PST 19 min. Proofs of Midpoint and Distance Formulas — In this lecture we will learn the Midpoint and Distance Formulas. MORE DETAILS…   ARCHIVED LECTURES BY SUBJECT ALGEBRA I   ALGEBRA II   BIOLOGY   CAHSEE   GEOMETRY   TRIG/PRE-CALC   © 2002 Renaissance Education Group, Inc. Home | Privacy Policy | Terms of Service