Triangles

A triangle is a polygon with exactly 3 sides. We say a triangle has six parts—its three angles and three sides. Thus a triangle can be classified by its angles or by its sides.

Classification of Triangles

By Angles

	Acute Triangle All three angles are acute angles.
	Right Triangle One of the three angles is a right angle.
	Obtuse Triangle One of the three angles is an obtuse angle.
	Equiangular Triangle All three angles are equal in measure.

By Sides

	Scalene Triangle No sides have same length.
	Isosceles Triangle Two sides have same length.
	Equilateral Triangle All three sides have same length.

Properties of Triangles

Triangles have so many properties that it is impossible to name them all here—I can only give you some of the most common ones.  

By Angles

The sum of the measures of the three angles of a triangle is 180°.

Corollary 

1. The measure of each angle of an equiangular triangle is 60°.
2. The measure of an exterior angle is the sum of the measures of the two remote interior angles.

By Sides

The sum of the lengths of any two sides is greater than that of the third side. 

Corollary 

1. The sum of the lengths of the two shortest sides is greater than that of the longest side. 
2. The difference of the lengths of any two sides is less than that of the third side. 

By Angles and Sides

The longest side of a triangle is opposite of its largest angle and the shortest side is opposite of the smallest angle and vice versa.

Corollary 

1. If two sides of a triangle have the same length, then the angles opposite them have the same measure, and vice versa. That is, the base angles of an isosceles triangle are congruent.
2. If the three sides of a triangle have the same length, then the three angles have same measure, and vice versa. That is, an equilateral triangle is equiangular and vice versa.

Pythagorean Theorem

In a right triangle, the square of the length of the hypotenuse is the sum of the squares of the lengths of the two legs.

More On Triangles

Ë Right Triangles

Ë Isosceles Triangles

Ë Congruent Triangles

Ë Similar Triangles

Ë Area of a Triangle