A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices. A triangle with three vertices says P, Q, and R is represented as △PQR. It is also termed a three-sided polygon or trigon. In this mini-lesson, we will explore everything about triangles, which are commonly seen around us. If you observe the shape of signboards and your favorite sandwiches it forms the shape of a triangle.
|1.||Parts of Triangle|
|2.||Classification of Triangle|
|3.||Properties of Triangle|
|5.||FAQs on Triangle|
Parts of Triangle
A triangle consists of various parts. It has 3 angles, 3 sides, 3 vertices. Let us learn the concept with the help of a triangle figure given below. Look at the triangle PQR.
In the above image:
- The three angles are, ∠PQR, ∠QRP, and ∠RPQ.
- The three sides are side PQ, side QR, and side RP.
- The three vertices are P, Q, and R
Classification of Triangle
According to two major elements, triangles can be classified as :
- On the basis of angles
- On the basis of the measurement of their sides.
Let us understand the classification of triangles with the help of the table given below. The table gives information about the difference between 6 different types of triangles on the basis of angles and sides.
Note: The sum of all the angles of the triangle is equal to 180°.
Properties of Triangle
Every geometry shape has fixed properties to identify the relationship between different sides and angles. In this section, we will study the important triangle properties listed below.
- Triangle has three sides, vertices, and angles.
- The angle sum property of a triangle states that the sum of the three interior angles of a triangle is always 180°. Such as in any given triangle PQR, angle P + angle Q + angle R = 180°.
- Triangle inequality property states that the sum of the length of the two sides of a triangle is greater than the third side.
- As per the Pythagorean theorem, in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides i.e., (Hypotenuse² = Base² + Altitude²).
- The side opposite the greater angle is the longest side.
- Exterior angle property of a triangle states that the exterior angle of a triangle is always equal to the sum of the interior opposite angles.
In geometry, for every two-dimensional shape, there are always two basic measurements we need to find out, i.e., the area and perimeter of that shape. Similarly, the triangle has two basic formulas which help us to determine its area and perimeter. Let us discuss the formulas in detail.
Perimeter of Triangle
The perimeter of a triangle is the sum of all three sides of the triangle. Consider △ABC.
In the above figure, the three sides of the triangle are represented as AB= c, AC = b, and CB = a respectively.
The perimeter of a triangle is the sum of all three sides AB + BC + CA.
Perimeter of Triangle formula = a + b + c units
Half of the perimeter of the triangle is termed as Semi Perimeter of Triangle. It is given as (a + b + c)/2 units.
Area of a Triangle
The area of a triangle is the space covered by the triangle. It is half the product of its base and altitude (height). It is always measured in square units, as it is two-dimensional. Look at the given triangle ABC.
Area of ΔABC = 1/2 × AD × BC square units.
Here, BC is the base and AD is the height of the triangle.
Important Notes on Triangle
- A triangle cannot have a measurement or value of all the angles less than 60°.
- A triangle is a 3-sided closed shape.
- There are two important formulas related to triangles, i.e., Herons formula and Pythagoras theorem.
- The sum of the angles of a triangle adds up to 180° and given as ∠1 + ∠2 + ∠3 = 180°.
☛Related Articles on Triangles
Check out these interesting articles to know more about triangles and topics related to triangles.
Example 1: The perimeter of a triangular garden is given as 26 feet. If two of its sides measure 7 feet and 11 feet respectively, what is the measure of the third side?
We know that the perimeter of a triangle is the sum of all three sides.
⇒ 26 = 7 + 11 + unknown side
Therefore, the unknown side is given by:
=26−(7+11) = 8 feet
∴ The third side of the given triangle measures 8 feet.
Example 2: Emma is building a triangular wooden birdhouse. If two of the angles measure 45° and 63°, what is the measure of the third angle?
We know that the sum of the angles of a triangle adds up to 180°. Therefore, the unknown angle is:
= 180° − (45° + 63°) = 72°
∴ The measurement of the third angle is 72°.
Example 3: The height of the triangular park is 360 feet and the side is 270 feet. Find the area of the park.
The height of the triangle = 360 feet and base = 270 feet
The area of a triangle is = 1/2 × Base × Height
Area of the triangular park = 1/2 × 270 × 360 = 48600 feet2
∴ Area of the triangular park = 48,600 feet2
FAQs on Triangle
What is the Triangle in Geometry?
In geometry, the triangle is defined as a two-dimensional shape with three sides, angles, and vertices, It is also considered as a polygon (trigon).
What are the Two Basic Triangle Formulas?
The two basic triangle formulas are the area of a triangle and the perimeter of a triangle. These triangle formulas can be mathematically expressed as;
- Area of triangle, A = [(½) base × height] square units.
- Perimeter of a triangle, P = (a + b + c) units
How many Types of Triangles are there in Maths?
There are basically six types of triangles categorized on the basis of sides and angles are listed below:
- Scalene triangle
- Isosceles triangle
- Equilateral triangle
- Acute angled triangle
- Obtuse angled triangle
- Right-angled triangle
Are Isosceles Triangles Always Acute?
No, an isosceles triangle can be an acute angle, right angle, or obtuse-angled triangle depending upon the measure of the angles it has.
What is the Area of the Scalene Triangle?
The area of the scalene triangle is used to find the area occupied by the scalene triangle within its sides. The area of the scalene triangle is half of the product of the base to the height of the scalene triangle. Thus, the area of the scalene triangle, with a base "b" and height "h" is given as "1/2 × b × h".
What is the Formula Used for Finding the Area of a Right Triangle?
The formula used for finding the area of a right triangle of base (b) and height (h) is 1/2 × base × height (or) 1/2 × b × h.
What is an Equilateral Triangle?
An equilateral triangle is a regular polygon (trigon) with three equal sides. Equilateral triangles also have three equal angles which measure 60 degrees each and sum up to 180 degrees.
What is an Isosceles Triangle?
In a triangle, if the length of only two sides is equal and the measure of corresponding opposite angles is also equal, then the triangle is said to be an isosceles triangle.
How are Triangle Worksheets Useful?
Triangle worksheets provide students an understanding of the concepts based on triangles. These worksheets can include types of triangles, classification of triangles, missing angles, properties of triangles, area and perimeter of triangles, and so on.
- Classifying Triangles Worksheets
- Missing Angles in Triangle Worksheets
- Area and Perimeter of Triangle Worksheets
What is a Right Triangle in Geometry?
A right triangle is a triangle with one angle measurement as 90 degrees (right angle). In geometry we have three different names for all the three sides of a right triangle which are listed below:
- The hypotenuse (longest side or the side opposite to 90° angle.)
- The base
- The perpendicular (altitude).