Archive for the ‘Geometry’ Category
Friday, November 20th, 2009
Interior Angles of Polygons
Description
A detailed tutorial on interior angles of polygons. Step by step tutorial including several examples of interior angles of polygons for reference.
Overview
There are two types of angles on a polygon: interior and exterior angles. In this tutorial, we will focus on interior angles. Interior angles are the angles that are found along the inside of the polygon. Interior angles may seem more difficult to find than exterior angles, because they don’t always add up to the same measurement of degrees. However, there is a formula that can be used to find the total measure of the interior angles. This formula is (n – 2) * 180 = D, where n is the number of sides on the polygon, and D is the total measure of the degrees.
Tags: 180, angle, concave, convex, degrees, formula, Geometry, Inside, interior, irregular, measure, negative, polygon, positive, regular
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Friday, November 20th, 2009
Exterior Angles of Polygons
Description
A detailed tutorial on exterior angles of polygons. Step by step tutorial including several examples of exterior angles of polygons for reference.
Overview
There are two types of angles on a polygon: interior and exterior angles. In this tutorial, we will focus on exterior angles. Exterior angles are the angles that are found when you draw a line of an angle on the outside of the polygon to form another angle. On a regular polygon, all the exterior angles should have the same measure. No matter what kind of polygon you have, the exterior angles will always add up to 360 degrees. Concave polygons are harder to find the measure of, because the exterior angles are negative, but they should still add up to 360 degrees. In order to find the measure of each individual exterior angle, simply use the formula 360 / n = D, where n is the number of sides, and D is the degree of each of the angles seperately. However, this formula only works for regular polygons, not irregular polygons.
Tags: 360, angle, concave, convex, degrees, exterior, formula, Geometry, irregular, measure, negative, Outside, polygon, positive, regular
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Thursday, November 19th, 2009
Finding the Altitude of a Triangle
Description
A detailed tutorial on how to find the altitude of a triangle. Step by step tutorial including several examples of how to find the altitude of a triangle for reference.
Overview
The altitude is just a way of saying the height of something. Typically, the term altitude is only used to refer to triangles. In triangles, the altitude is a little different from the height. Unlike the height, the altitude can be taken from three points of the triangle – it can be taken through the center of any of the three vertexes of the triangle. The altitude goes from the vertex to the line across from it, forming a right angle with that line. All three altitudes should intersect at a common point in the center of the triangle, known as the orthocenter.
Tags: altitude, angle, center, edge, Geometry, height, intersect, line, orthocenter, perpendicular, point, triangle, vertex
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Tuesday, November 17th, 2009
Definition of a Bisector
Description
A detailed tutorial on the definition of a bisector. Step by step tutorial including several examples of bisectors for reference.
Overview
A bisector is any line that evenly divides a symmetrical shape or object. The only difference between the bisector and the test for symmetry is that when testing for symmetry, the line is not really there. A bisector is really there. The most common kind of bisector is an angle bisector. In order to remember bisectors, think of them as perpendicular lines that cross right in the middle.
Tags: angle, bisector, cross, divides, evenly, Geometry, line, middle, object, perpendicular, shape, symmetrical, symmetry, test
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Tuesday, November 17th, 2009
Introduction to Half-Planes
Description
A detailed tutorial on half-planes. Step by step tutorial including several examples of half-planes for reference.
Overview
A half-plane is simply half a plane, that includes all the lines on half of the plane and sometimes the points. If the plane includes the points, it is a closed half-plane. If it doesn’t, then it is an open half-plane. The most common half planes are upper, lower, right, and left planes, where that side of the plane is all that is included. However, there are many other kinds of half planes that are all a variety of diagonal half-planes.
Tags: bottom, closed, Geometry, half, half-plane, left, lines, lower, open, plane, points, region, right, top, upper
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Tuesday, November 17th, 2009
How to Find Slant Height
Description
A detailed tutorial on how to find the slant height. Step by step tutorial including several examples of how to find the slant height for reference.
Overview
The slant height is an additional measure of height that is used for the different types of triangular prisms. The common traingular prisms are your typical pyramid, and cones. On a pyramid, the slant height is the height of one of the triangular faces. On a cone, the slant height is to be found using a formula that is only for the cone. It is the square root of the radius squared added to the real height squared.
Tags: 3D, base, cone, face, figure, geometrical, Geometry, height, polyhedron, prism, pyramid, shape, side, slant, triangle, triangular
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Tuesday, November 17th, 2009
Overview of Sides and Bases of Polyhedrons
Description
A detailed tutorial on sides and bases of polyhedrons. Step by step tutorial including several examples of sides and bases of polyhedrons for reference.
Overview
Sides and bases of polyhedrons are more commonly known as faces of 3D geometrical shapes. Typically on a polyhedron you will have 2 bases and several sides, although there are exceptions to that rule. The cylinder only has one side, and the triangular prism, or pyramid, only has one base. You can identify the base because it is a unique shape on the polyhedron. Everything else is a side. This only applied to your normal polyhedron shapes such as prisms.
Tags: 3D, bases, cylinder, faces, figure, geometrical, Geometry, polyhedron, prism, rectangular, regular, shape, sides, triangular, unique
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Tuesday, November 17th, 2009
Overview of Half-Circles
Description
A detailed tutorial on equations of a half-circle. Step by step tutorial including several examples and an explanation of half-circles for reference.
Overview
A half-circle is truely half of a circle. If you take a circle and cut it in half, you will get a half circle. Because of this, the equations of the half-circle are very similar to the equations of a full circle – simply divide the equation by two. The only ones that you cannot find that way are the radius, diameter, and circumference. The radius and diameter do not change on a half-circle. There is no circumference on the half-circle, but if you need the circumference for another formula you can use the circumference of the whole circle of that half-circle.
Tags: area, basic, circle, circumference, coordinates, cut, diameter, divide, equation, Geometry, half, half-circle, pi, radius, shape, split, two, whole
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Friday, November 13th, 2009
Introduction to Aspect Ratio
Description
A detailed tutorial on what aspect ratio is. Step by step tutorial including several examples of how to find the aspect ratio for reference.
Overview
The aspect ratio can only be used when referring to a shape, typically a square type of shape, such as a square, rhombus, rectangle, or parallelogram. The aspect ratio is used very often for describing measurements. It is the ratio of the longer dimension to the shorter dimension – that is, the length to the width. In a 3D shape, the depth – which is the second measurement of width – is added to the end of this measurement.
Tags: 2D, 3D, aspect, depth, Geometry, length, measure, measurement, parallelogram, ratio, rectangle, rhombus, shape, square, width
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Friday, November 13th, 2009
An Overview of Composite Solids
Description
A detailed tutorial on what a composite solid is. Step by step tutorial including several examples of composite solids for reference.
Overview
A composite solid is exactly the same as a composite figure, only it is in 3D instead of in 2D. It is any kind of polyhedron (like a prism or a pyramid) that can be split into two or more of the basic types of polyhedrons in order to solve for the volume of the figure. Composite solids are very rare, and there are no regular types of solids that would be considered a composite solid.
Tags: 2D, 3D, area, basic, composite, difference, dimension, figure, Geometry, polyhedron, prism, pyramid, rare, solid, split, types, volume
Posted in Geometry | No Comments »
