Triangle and It’s Properties – Definition and Types

Triangle – Definition and Types

A triangle is a two-dimensional, closed figure that has three line segments, called sides, that intersect at three angles, called vertices. The sum of the angles in a triangle is always 180 degrees.

There are three types of triangles: equilateral, isosceles, and scalene.

An equilateral triangle is a triangle in which all three sides are the same length.

An isosceles triangle is a triangle in which two of the sides are the same length.

A scalene triangle is a triangle in which all three sides are different lengths.

What is the Triangle?

The triangle is one of the basic shapes in geometry. It is a three-sided polygon. The three sides are called angles. The angles always add up to 180 degrees. The triangle is the simplest polygon.

Types of Triangles

There are three types of triangles: acute, right, and obtuse.

An acute triangle has three acute angles.
A right triangle has one right angle.
An obtuse triangle has one obtuse angle.

What are the Properties of Triangles?

Triangles have three sides and three angles. The angles of a triangle always add up to 180 degrees. The longest side of a triangle is called the “base” and the other two sides are called “legs”.

Other Polygons

There are other polygons that are not mentioned above.

Some other polygons are:

-Trapezoid
-Semicircle
-Hexagon
-Octagon
-Pentagon

Tips to study Triangles

1. Draw triangles and identify the angles and sides.

2. Find the angles and sides of a triangle given one angle and two sides.

3. Find the angles and sides of a triangle given two angles and one side.

4. Find the perimeter and area of a triangle.

5. Find the angles of a triangle if the lengths of two sides and the enclosed angle are given.

6. Find the lengths of the sides of a triangle if the angles are given.

7. Find the equation of the line containing the two vertices of a triangle.

triangle Properties

The properties of the triangle are:

• The sum of all the angles of a triangle (of all types) is equal to 180°.
• The sum of the length of the two sides of a triangle is greater than the length of the third side.
• In the same way, the difference between the two sides of a triangle is less than the length of the third side.
• The side opposite the greater angle is the longest side of all the three sides of a triangle.
• The exterior angle of a triangle is always equal to the sum of the interior opposite angles. This property of a triangle is called an exterior angle property.
• Two triangles are said to be similar if their corresponding angles of both triangles are congruent and the lengths of their sides are proportional.
• Area of a triangle = ½ × Base × Height
• The perimeter of a triangle = sum of all its three sides

Triangle Formula

• Area of a triangle is the region occupied by a triangle in a two-dimensional plane. The dimension of the area is square units. The formula for area is given by;

Area = 1/2 x Base x Height

• The perimeter of a triangle is the length of the outer boundary of a triangle. To find the perimeter of a triangle we need to add the length of the sides of the triangle.

P = a + b + c

• Semi-perimeter of a triangle is half of the perimeter of the triangle. It is represented by s.

s = (a + b + c)/2

where a, b and c are the sides of the triangle.

• By Heron’s formula, the area of the triangle is given by:

A = √[s(s – a)(s – b)(s – c)]

where ‘s’ is the semi-perimeter of the triangle.

• By the Pythagorean theorem, the hypotenuse of a right-angled triangle can be calculated by the formula:

Hypotenuse² = Base² + Perpendicular²