 # Triangle and It’s Properties

You may have come across the word ‘triangle’ several times in your life. You may also know how its shape is and how it varies from a square or a circle. However, this article sheds light on what a triangle is in the context of mathematics.

On top of that, you will also come to know about the triangle and its properties class 7. Therefore, it will make you excited when you find how easy it is to understand the underlying concepts in this chapter. However, first know what a triangle is in a mathematical sense.

What is the Triangle?

Triangles fall under the category of geometry in mathematics. In other words, it has a unique shape that differentiates it from different geometrical shapes that you see in everyday life. However, a triangle is mainly a closed polygon which has three straight sides.

Take a look at the following diagram:

In this figure, you will see three line segments AB, BC, and AC joined at their ends. Additionally, ‘triangle’ means a figure that has three angles, as you can see in this diagram. The three angles are thus ⊿BAC, ⊿ABC, ⊿ACB.

You will find it intriguing to know that no matter what the angles are in a triangle, their sum is always 1800. Therefore, this polygon can only exist if the total of the internal angles adds up to 1800. You can refer to this phenomenon as sum property of a triangle.

Now, take a look at the types of triangles to understand class 7 the triangle and its properties better.

You can classify the types of triangles in the following categories:

## Types of Triangles

 Types of Triangles Definition Properties Based on Internal Angles: 1. Acute-angled Triangle In this kind of a triangle, the angles on all three edges are less than 900. Since the angles are below 900, they are acute. Each of the angles is below 900, and the sum of those angles is always 1800. 2. Right-angled Triangle In this category, at least one angle of the triangle has a dimension of 900. Since 900 is widely known as a right angle, a triangle that has one such angle is called a right-angled triangle. One side being 900, the other angles have to be acute. It is because the addition of all internal angles always produce 1800. On the other hand, the side opposite to the largest angle is the longest side. You can also call it a hypotenuse. 3. Obtuse-angled Triangle In this case, the triangle has only one angle that is greater than 900. You can also call it an oblique angle. Naturally, the other two angles have to be smaller than an obtuse angle. It is so that the internal sum of all the angles remains 1800. Based on Length: 1. Equilateral Triangle As the name suggests, all three sides of this type of a triangle are equal in length. Therefore, the angles within the triangle also have to be identical. Since the internal angles add up to 1800, each angle has to be equal in an equilateral triangle. In this case, each angle of this triangle is 600. 2. Isosceles Triangle In this category of triangles, two sides have equal lengths. As a result, the underlying angles on each side are also equal. Since two sides have the same length, the third side has to have a different length. On top of that, the angle of the other side is also dissimilar to the previous angles. 3. Scalene Triangle In a scalene triangle, none of the three sides has equal lengths. Therefore, their angles are not equal to each other as well. In this case, the lengths of the three sides are diverse. However, the sum of dissimilar internal angles also has to be 1800.

The table above concludes the class 7 maths chapter the triangle and its properties. However, you should also know about the additional features of these types of triangles. You can gather knowledge from the following section.

What are the Properties of Triangles?

Take a look at the following triangle and its properties –

• The word ‘vertices’ refer to the pointed edges of a triangle.

• Always remember that when you add two sides of a triangle, the sum will come out to be higher than the third side’s length.

• The side mirroring the largest angle is always the longest line segment in a triangle. In case of right angle triangle, you can call that side as a hypotenuse. The equation to find the hypotenuse is:

(Hypotenuse)2 = (Perpendicular)2 + (Base)2. It is known as the Pythagoras Theorem.

• The area of a triangle is = 12 X Height X Base.

• The sum of all the line segments in a triangle is known as its perimeter.

• The sum of an interior angle and the adjacent exterior angle of a triangle is always 1800

These are the primary triangle and its property. However, try and answer the following questions:

1. Can a triangle have two right angles?

2. Can a triangle have two obtuse angles?

3. Can a triangle have three angles equal to 600

1. What is a Triangle?

Ans. A triangle refers to a two-dimensional polygon that has three line segments joined at the end. Additionally, the edges of a triangle are called vertices. Triangle is one of the basic shapes that can be found in geometry.

Triangles are categorised according to the lengths of their sides. You will find equilateral triangle, that carries all three sides of exact same length. You will also come across isosceles triangles, which carries only two sides of equal length. Isosceles triangles also has two angles of exact same measure; these are usually the two angles sitting opposite of the sides with equal length.

2. What are the Types of Triangles?

Ans. One can classify the types of triangles into two categories, angle-based and length-based. In angle-based triangles, the various types are acute-angled triangle, obtuse-angled triangle, and right-angled triangle. On the other hand, you can divide length-based triangles into equilateral, isosceles, and scalene triangle.

Right-angled triangles has one of it’s inside angle at 90°. The side opposite to the right angle is known as a hypotenuse, which is the longest side of the triangle. These triangles follow the Pythagorean theorem, where the square of the hypotenuse’s length is equal to the sum of the square of the length of other two sides.

3. What is the Sum of all the Interior Angles of a Triangle?

Ans. The addition of all the interior angles within a triangle is always 1800. It follows Euclid’s parallel postulate. These were first introduced around 300 BC, in his books, Elements.

Triangles are usually considered as two-dimensional figures, unless it is a non-planar triangle. The addition of the interior angles, also known as Euclidean space, is fixed, which allows you to measure an angle if the value of other two angles are provided. The sum of all three exterior angles of every triangle is 360°.

4. What is a Right-angled Triangle?

Ans. A right-angled triangle refers to a specific type of a geometric pattern where out of the three angles, one is 900.

Right-angled triangles show several unique characteristics, such as the relation between the legs and its angles. If the legs of right-angled triangles have same length, the angles opposite to those two legs will be measured the same. Right-angled triangles follow Pythagorean theorem, where the length of its hypotenuse is equal to the root square of the length of its leg.