Triangles

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Triangles:

A.  Definitions

isosceles triangle - A triangle that has at least two sides that are equivalent.

equilateral/equiangular triangle - A triangle that has all three sides equal and all 3 interior angles are 60 degrees.

acute - An acute angle is an angle that is less than 90 degrees.  An acute triangle is a triangle where all the angles are less than 90 degrees.

obtuse - An obtuse angle is an angle that is more than 90 degrees.  An obtuse triangle is a triangle where one angle is more than 90 degrees.

right - A right angle is an angle that is exactly 90 degrees.  A right triangle is a triangle where one angle is 90 degrees.

complement - The compliment of an angle is 90 minus the angle.  In other words, the two angles must equal a right angle.

supplement - The supplement of an angle is 180 minus the angle.  In other words, the two angles must add to be 180 degrees.

B.  Basic Memorizations

General Triangles:

Area = 1/2bh, where 'b' is the base and 'h' is the height

Perimeter = a+b+c, where 'a', ' b', and 'c' are the sides

 

Right Triangles:

Area = 1/2ab, where 'a' and 'b' are the legs of the triangle

c = , where 'c' is the hypotenuse

 

Equilateral Triangles:

Area = , where 'h' is the height

Area = , where 's' is the side

C.  Examples

Ex [1]  Find the area of an equilateral triangle with sides of 8cm.  __________cm2.

a.  In this example you should use the formula

b.  82 = 64.  64 4 = 16.

c.  The answer is .

Ex [2]  The complement of is ______ degrees.

a.  The complement of an angle is the angle that when added to it is 90 degrees.

b.  Therefore, the answer is 90 - 76 = 14.

c.  The answer is 14.

 

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