Triangle

A triangle is a polygon determined by three nonaligned points (vertices) or three intersecting line segments (sides).

The vertices of a triangle are written with capital letters.

The sides of a triangle are lowercase and correspond with the letters of the opposite vertices.

The angles of a triangle can be written like the vertices or with Greek letters.

Types of Angles

Interior angles are formed by two sides.

Exterior angles are formed on one side and its extension.

Properties of Triangles

1. One side of a triangle is less than the sum of the other two and greater than their difference.

a < b + c

a > b − c

2.In a triangle, the greatest angle is always opposite the longest side.

3. If a triangle has two equal sides, its opposite angles are also equal.

4. The sum of the interior angles of a triangle equals 180°.

A + B + C = 180º

5.  The value of an exterior angle of a triangle equals the sum of the two nonadjacent interior angles.

α = B + C

6.   The interior and exterior angle of a triangle at a particular vertex are supplementary, that is to say, they add up 180º.

α = 180º − A

Equal Triangles

1.Two triangles are equal when they have the same sides and two adjacent angles match.

2.Two triangles are equal when they have two equal sides and the angle between them is the same.

3.Two triangles are equal when the three sides are equal.

Types of Triangles by Sides

Equilateral Triangle

Three equal sides.

Two equal sides.

Scalene Triangle

Three unequal sides.

Types of Triangles by Angles

Acute Triangle

An acute triangle has three acute angles.

Right Triangle

A right triangle has a right angle.

The longest side of the triangle is called the hypotenuse.

The shorter sides of the triangle are the legs or catheti (singular: cathetus).

Obtuse Triangle

An obtuse triangle has an obtuse angle.

Perimeter of a Triangle

 Equilateral Triangle Isosceles Triangle Scalene Triangle

Area of a Triangle

Example

Find the area and perimeter of the following triangle:

P = 2 · 11 + 7.5 = 29.5 cm