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Triangles
Definitions and properties of triangles in geometry.
Angles of a Triangle
A triangle is a closed plane figure with three (straight) sides.
The sum of all three interior angles of a triangle is equal to 180°.
Isosceles Triangle
An isosceles triangle is a triangle with two equal sizes.
In the above triangle sides AC and BC are equal and therefore angles A and B are also equal.
Equilateral Triangle
An equilateral triangle has all sides and all angles are equal in size.
All angles of the triangle are equal to 60°.
Right Triangle
A right triangle has a right angle.
c is the hypotenuse, a and b are the sides of the triangle.
Pythagorean Theorem
In any right triangle with hypotenuse c and sides a and b we have:
c
^{ 2}
= a
^{ 2}
+ b
^{ 2}
Sine law in a Triangle
Triangle without right angle may be solved using sine law expressed as follows
a / sin(A) = b / sin(B) = c / sin(C)
Cosine law in a Triangle
The cosine is alos used to solve traingles without right angle. The cosine law is expressed as follows:
a
^{ 2}
= b
^{ 2}
+ c
^{ 2}
- 2 b c cos(A)
or
b
^{ 2}
= a
^{ 2}
+ c
^{ 2}
- 2 a c cos(B)
or
c
^{ 2}
= b
^{ 2}
+ a
^{ 2}
- 2 b a cos(C)
More References and Links to Triangles
Triangle Problems
Geometry Tutorials, Problems and Interactive Applets.
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