Geometry

Other Polygons

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What is a polygon?

Regular polygons

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In a regular polygon, all sides are the same length.(All regular polygon images hosted at http://www.mathleague.com/help/geometry/polygons.htm)

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Irregular polygons

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In an irregular polygon, not all sides are the same length.(All irregular polygon images hosted at http://www.mathleague.com/help/geometry/polygons.htm)

Pentagon

Hexagon

Heptagon

Octagon (8 sides)

Nonagon (9 sides)

Decagon

Glossary Page

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Triangles

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Types of Triangles

Organized by side length

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Summary:3 sides the same length: equilateral2 sides the same length: isoscelesNo sides the same length: scalene

Equilateral

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An equilateral triangle has all three sides the same length. Also, all of the angles are 60° angles.(image hosted at http://www.mathsisfun.com/triangle.html)

Isosceles

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An isosceles triangle has two sides the same length, and the angles opposite those two sides are also equal.(image hosted at http://www.mathsisfun.com/triangle.html)

Scalene

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A scalene triangle has three sides with different lengths. Also, all three angles have different measures.(image hosted at http://www.mathsisfun.com/triangle.html)

Organized by largest angle

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Summary:Largest angle > 90°: ObtuseLargest angle = 90°: RightLargest angle < 90°: Acute

Acute

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In an acute triangle, all three angles measure less than 90°.(image hosted at http://www.mathsisfun.com/triangle.html)

Right

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In a right triangle, one angle measures exactly 90°.(image hosted at http://www.mathsisfun.com/triangle.html)

Obtuse

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In an obtuse triangle, one of the angles measure more than 90°.(image hosted at http://www.mathsisfun.com/triangle.html)

Special right triangles

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Summary: 30/60/90 triangle Side opposite 90°: x Side opposite 60°: x√(3)/2 Side opposite 30°: x/2 45/45/90 triangle Side opposite 90°: x Sides opposite 45°: x√(2)/2

30/60/90

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Summary:Length of hypotenuse: xLength of side opposite 30°: x/2Length of side opposite 60°: x√(3)/2 orLength of hypotenuse: 2xLength of side opposite 30°: xLength of side opposite 60°: x√(3)These are equivalent representations, depending on whether x is the short side or the hypotenuse (long side).

45/45/90

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Summary:If the length of the hypotenuse is x, the other two sides are of length x√(2)/2.

Area Formulas

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There are over 100 formulas for finding the area of a triangle.The three most commonly used ones are:Basic Formula: A = bh/2 b is the base h is the heightUsing Trigonometry: A = ab sin(C) / 2 a is the length of one side b is the length of another side C is the angle between the two known sidesHeron's Formula (also called Hero's Formula): A = square root of: [s(s-a)(s-b)(s-c)] a, b and c are the three side lengths s is the semiperimeter: s = (a+b+c)/2

Basic

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Using Trigonometry

Heron's Formula

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Other Formulas

Quadrilaterals

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Kites

Trapezoids

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A trapezoid has one pair of parallel sides.(Image hosted at http://www.mathleague.com/help/geometry/polygons.htm)

Cyclic Quadrilaterals

Glossary Page

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Parallelograms

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A parallelogram has two pairs of parallel sides. (Image hosted at http://www.mathleague.com/help/geometry/polygons.htm)

Rectangles

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A rectangle is a quadrilateral with four 90° angles.(Image hosted at http://www.mathleague.com/help/geometry/polygons.htm)

Squares

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A square is a rectangle where all four sides are the same length.(Image hosted at http://www.mathleague.com/help/geometry/polygons.htm)

Rhombuses

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A rhombus is a parallelogram where all four sides are the same length.(Image hosted at http://www.mathleague.com/help/geometry/polygons.htm)

Squares

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A square is a rectangle where all four sides are the same length.(Image hosted at http://www.mathleague.com/help/geometry/polygons.htm)