A triangle is a specific polygon that has sides and three angles, three vertices. In this article, we are going to learn about the properties of triangles with examples and brief explanations. Depending upon the length of the sides and angles, the triangles are classified into six types. Scroll down this page to know about the types and properties of triangles. Thus the students of 5th grade can use this article as a reference and practice well for the exams.

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## Triangle – Definition

A triangle is a polygon that has three sides and angles. It has three line segments joined end to end.

### Types of Triangle

A triangle is classified into two ways,
i. Triangle-based on their sides
ii. Triangle-based on their angles

Based on the sides:
i. Equilateral triangle
ii. Isosceles triangle
iii. Scalene triangle

Based on the angles:
i. Acute triangle
ii. Obtuse triangle
iii. Right triangle
Scalene Triangle: All the sides and angles are unequal.
Isosceles Triangle: It has two equal sides. Also, the angles opposite these equal sides are equal.
Equilateral Triangle: All the sides are equal and all the three angles equal to 60°.
Acute Angled Triangle: A triangle having all its angles less than 90°.
Right Angled Triangle: A triangle having one of the three angles exactly 90°.
Obtuse Angled Triangle: A triangle having one of the three angles more than 90°.

### Triangle Formula

The basic properties of triangles such as area and perimeter are given below.
Area of a triangle: The total amount of space inside the triangle is called the area of a triangle. The units to measure the area of a triangle is square units.
A = 1/2 × base × height
The perimeter of a triangle: It is the measure of the outside of the triangle. The perimeter of a triangle is the sum of the lengths of the sides
P = a + b + c

### Properties of Triangle

The properties of the triangle are as follows,

1. The sum of the length of the two sides of a triangle is greater than the length of the third side.
2. The sum of all the angles of a triangle is equal to 180°.
3. The side opposite the greater angle is the longest side of all the three sides of a triangle.
4. The difference between the two sides of a triangle is less than the length of the third side.
5. The exterior angle of a triangle is always equal to the sum of the interior opposite angles.
6. Area of a triangle = 1/2 × Base × Height
7. Two triangles are said to be similar if the corresponding angles of both triangles are congruent and the lengths of their sides are proportional.
8. This property of a triangle is called an exterior angle property.
9. The perimeter of a triangle = sum of all its three sides.

### Triangle Properties Examples with Answers

Example 1.
A triangle has ________ vertices and ______ sides.
Solution:
A triangle has three vertices and three sides.

Example 2.
The sum of the measure of three angles of a triangle is ____
Solution:
The sum of the measure of three angles of a triangle is 180 degrees.

Example 3.
Find the measure of three angles of a triangle ∠A = 60°, ∠B = 60°, ∠C = 60°
Solution:
Use the property ‘The sum of the measure of three angles of a triangle is 180 degrees.’
∠A + ∠B + ∠C = 180°
60° + 60° + 60° = 180°
Thus the given angles is equilateral angle.

Example 4.
The two angles of a triangle are ∠A = 80°, ∠B = 70°. Find the measure of the third angle.
Solution:
Given,
The two angles of a triangle are ∠A = 80°, ∠B = 70°.
Use the property ‘The sum of the measure of three angles of a triangle is 180 degrees.’
∠A + ∠B + ∠C = 180°
80° + 70° + x° = 180°
150° + x° = 180°
x° = 180° – 150°
x° = 30°
Thus the measure of the third angle is 30°.

Example 5.
The two angles of a triangle are ∠B = 45°, ∠C = 70°. Find the measure of the third angle.
Solution:
Given,
The two angles of a triangle are ∠B = 45°, ∠C = 70°.
Use the property ‘The sum of the measure of three angles of a triangle is 180 degrees.’
∠A + ∠B + ∠C = 180°
∠A + 45° + 70° = 180°
∠A = 180° – 115°
∠A = 65°
Thus the measure of the third angle is 65°.

### FAQs on Properties of Triangle

1. How many properties of the Triangle are there?

All the properties of a triangle are based on its sides and angles. By the definition of triangle, we know that it is a closed polygon that consists of three sides and three vertices.

2. What is the use of properties of triangles?

The triangle is a closed polygon that has three angles, sides, and vertices. Based upon the length of sides and measure of angles, the triangles are classified into different types of triangles. Properties of a triangle help us to identify a triangle from a given set of figures easily and quickly.

3. What are the five properties of triangles?

• It has three sides, three vertices, and three angles.
• The Sum of all three angles equals 180 degrees.
• The sum of the length of any two sides of a triangle is always greater than the third side.
• The perimeter of the triangle is equal to the sum of all three sides.
• The area of a triangle is equal to half of the product of base and height.