Geometry-High School |
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Introduction to Geometry Euclid have you stumped? Archimedes run rings around your head? Well you've come to the right place. This is where you'll find almost everything you'll ever need to know about Geometry. We have a special page on constructions and plenty of sample problems to help you understand the concepts. Have a blast and don't forget to check out our Glossary - it's huge!
Geometry Basics Visit the Math League to understand the basics of Geometry, including basic terms, angles, figures and polygons, area and perimeter, coordinates, space figures and basic solids.
The Pythagorean Theorem The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. The Pythagorean Theorem is a statement about triangles containing a right angle. The Pythagorean Theorem states that: "The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides."
Geometry This site covers many aspects of geometry, from the basics to very advanced.
Math.com Homework Help: Geometry This is a detailed site dealing with many areas of geometry, including coordinate geometry, angles and lines, polygons and more!
Math for Morons- Geometry On this and the following pages, we'll try to clear up some of the common problems people have with geometry (which seems to stump just about everyone who's ever taken it). Everything from parallel lines to volumes of prisms and a couple of word problems are covered.
Lessons on Perimeter and Area of Polygons A variety of polygons are used in these lessons. Every example is accompanied by a labeled diagram. Whole numbers are used throughout these lessons.
Figures and polygons A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.
NOVA Online: Pythagorean Theorem Puzzle On the diagram, show that a^{2} + b^{2} = c^{2}, by moving the two small squares to cover the area of the big square.
Annotated Animated Proof of the Pythagorean Theorem Check out this animated site that proves the Pythagorean Theorem.
Right Triangle Trigonometry If a right triangle is superimposed on a coordinate system with one of the acute angles in standard position, then one gets the following right triangle-based definitions of the the trigonometric functions. . .
Theorems Unique to the Right Triangle When you look at theorems involving right triangles, many textbooks will list three or four. But, in the end, most of those would have to be based on more general theorems such as Angle - Angle - Side. There are four theorems that apply to all triangles and thus using these for right triangles is just extra problems that might confuse some students. But, it is always good for the students to review old material and so this will cover all the theorems.
Angles and angle terms Two rays that share the same endpoint form an angle. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.
Angle Explorations --Interactive Applets Drag the red point A. Observe how the measure of angle B changes. What is the sum of the angles of a triangle? Is it true for any triangle?
Plane Geometry This site gives you everything from basic definitions to theorems and reasoning in Geometry.
Conic Sections A conic section is the intersection of a plane and a cone. By changing the angle and location of intersection, we can produce a circle, ellipse, parabola or hyperbola; or in the special case when the plane touches the vertex: a point, line or 2 intersecting lines.
Conic Sections This applet allows you to specify a plane in three-dimensional space. The applet plots the intersection of the plane with a cone whose sides have unit slope. When in range, the intercepts of the plane are indicated by blue dots on the axes.
Webmath: Conic Sections Plug your equation into the solver and graph your circle, parabola, ellipse, or hyperbola.
Symmetry in the Plane An overview of rotation, translation, reflection, and glide reflection including diagrams illustrating the four symmetries and questions that could be used with students. The site also includes a step-by-step lesson plan using paper, pencil, and protractor to explore reflections in the plane.
Working with Dilations Answer the following questions dealing with dilations and coordinate geometry.
The Binomial Expansion and Infinite Series Pascal's triangle of numbers, although named after Pascal, was known much before his time. If there is one piece of mathematics that exhibits many patterns, this is it. There are triangular numbers and tetrahedral numbers, and even the Fibonacci numbers are in it.
Visualizing An Infinite Series This site has an example of an infinite geometric series. Infinite, because it has an infinite number of terms. Geometric, because the ratio of any two consecutive terms is a constant.
Mathcad Activities on Infinite Series and Taylor Polynomials To enhance our students' learning of the infinite series material, a computer laboratory activity devoted to the subject was created. In the Summer 1994, the author developed computer activities intended to provide an intuitive interpretation to some of the fundamental notions involved in studying infinite series and Taylor polynomials. These activities are described in the following sections.
Infinite Series from Wikipedia An infinite series is a sum of infinitely many terms. Such a sum can have a finite value, and if it has, it is said to converge.
Introduction to Vectors In this tutorial we will examine some of the elementary ideas concerning vectors. Graphically, a vector is represented by an arrow, defining the direction, and the length of the arrow defines the vector's magnitude.
Vectors in a Plane Take in the plane a fixed origin O. A translation t in the plane, is now completely determined by the image point P of O by this translation. The translation is determined by point P or also by any couple points (A,B) so that t(A)=B .
Math Help: Working with Vectors The following fast-loading webpages describe some properties and physical applications of vectors. Each section builds on the previous ones to make a logical sequence and I have used hot links within sections so that it is easy to refer back if you want to.
Vector Operations Vectors may be added, subtracted, multiplied by regular numbers (scalars), and multiplied with each other in two different ways. These operations will now be briefly reviewed.
Adding vectors Since we can think of vectors as displacements or journeys, to add two vectors we just need to find the single displacement which gives the same result as doing the two displacements separately.
Multiplying Vectors The definition of the vector product of two vectors is in terms of the angle q between them, as with the scalar product. This time the definition is a b = |a||b| sin(q)n.
Geometry Basic Terms Get the basics about lines, points, intersection, line segments, rays, endpoints and parallel lines.
Geometry Glossary In this glossary I'll define most of the words you'll ever need in geometry. You'll also see some algebra terms, and maybe some trig terms.
All About Measurements These pages teach measurement operations. Each page has an explanation, interactive practice and challenge games about geometry.
The English System of Measurement The English system of measurement grew out of the creative way that people measured for themselves. Familiar objects and parts of the body were used as measuring devices. Eventually, a standard was set so that all measurements represented the same amount for everyone.
The Metric System of Measurement In the metric system, each of the common kinds of measure -- length, weight, capacity -- has one basic unit of measure. To measure smaller amounts, divide the basic unit into parts of ten, a hundred, or a thousand, and so on. To measure larger amounts, multiply the basic unit by ten, a hundred, or a thousand, and so on.
IFP Metric Conversion Tables The tables at this site provide for conversion from/to metric and imperial and US measurement systems.
((x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}) Measurement Formulas Here are some measurement formulas from the different parts of geometry. You'll find some two-dimensional and some three-dimensional formulas.
Coordinates and similar figures Coordinates are pairs of numbers that are used to determine points in a plane, relative to a special point called the origin.
Ask Dr. Math - High School Level Questions and Answers about math topics at the high school level.
Geometry Lessons Each of the lessons includes a section of teaching, then a short assignment, and then an answer page so you can correct your answers.
Area and perimeter The area of a figure measures the size of the region enclosed by the figure. This is usually expressed in terms of some square unit. A few examples of the units used are square meters, square centimeters, square inches, or square kilometers.
Space figures and basic solids A space figure or three-dimensional figure is a figure that has depth in addition to width and height. Everyday objects such as a tennis ball, a box, a bicycle, and a redwood tree are all examples of space figures.
Areas, Volumes, Surface Areas Check out this site to see formulas for areas, volumes, and surface areas of different shapes.
Lessons on Circumference and Area of Circles These lessons explain the meaning of Pi, circumference, and area through real life connections that students can relate to. Both decimal and whole-number answers are required.
The Geometry of the Sphere A sphere is a set of points in three dimensional space equidistant from a point called the center of the sphere. The distance from the center to the points on the sphere is called the radius of the sphere.
Squares, Cubes, and Square Roots In math, you often must multiply a number by itself. A good example is when you compute the area of a square. . .
Squaring the Circle The circle is one of the enigma's of mathematics. It is defined as the set of points in a given plane at a given distance from a center point. From a practical position, a compass is an excellent tool for describing such a circle.
Circumference and Area Problems from Real Life This site contains questions on circumference and area. Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect.
Math Forum - Geometry Problem of the Week Check out this online library of geometry problems. There is a new problem every week as well as an archive of past problems.
Math Forum - Geometry Project of the Month Check out this online library of geometry projects. There is a new project every month as well as an archive of past problems.
Geometry Sample Problems The problems at this site should be considered slightly above average in terms of difficulty. Answers are on the answer page, and links are provided to each specific answer.
Lesson Plans/Classroom Activities
Discovering Growth Patterns
Noon Project Revisited
Angles-Water to the Max
What is Pi?
Travel Triangles
Finding the Sum of the Exterior and Interior Angles of a Polygon
Polygons Made to Order
Properties of Quadrilaterals
Significant Figures
How Many Regular Polyhedrons Are There In This or Any Universe?
Exploring Geometry on the Sphere
Similarity
Exploring Similarity Using Scale Drawings
Circumferences, Diameters, and Radii
The Area of a Circle
Measurement of Volume
Measuring the Earth
The Surface Area of a Cylinder
Metric System
Metric Equivalents
L to L: Additional Lesson Plans/Classroom Activities