Triangles

Definitions and properties of triangles in geometry.

Angles of a Triangle

A triangle is a closed plane figure with three (straight) sides.
Triangle
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.
Isosceles Triangle
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.
Equilateral Triangle
All angles of the triangle are equal to 60.

Right Triangle

A right triangle has a right angle.
Right Triangle

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
Triangle

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.