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Triangle and It’s Properties

Maths

Triangle and It’s Properties

Reviewed by:

Rama Sharma

Triangle – Definition and Types

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:

(Image will be Uploaded Soon)

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:

Can a triangle have two right angles?
Can a triangle have two obtuse angles?
Can a triangle have three angles equal to 600?

Now that you know about the triangle and its properties, read about similar interesting topics on Vedantu’s website. You can also download our Vedantu app for enhanced access to these materials.

Other Polygons

Polygons are characterized as closed 2-dimensional shapes that are formed by joining 3 or more line segments with one another. Polygons can be classified as-

Regular Polygons- Regular Polygons are polygons with all of the sides associated with them, tend to be equal, and all the interior angles measure the same. For Example- A Square is a regular quadrilateral or a regular polygon with 4 sides and all its angles are 90 degrees., etc.

Concave Polygons- Concave Polygons are polygons with a minimum of one angle that measures more than 180 degrees. The vertices of these types of polygon tend to be inwards but can also point outwards.

Convex Polygons- Convex Polygons are polygons in which all the interior angles of the figure are less than 180 degrees. Convex Polygons are exactly the opposite of the concave polygon. The vertices of a convex polygon are always towards the out direction.

Trigons- Trigons, also known as Triangles, are polygons that possess three sides. These trigons are divided into different types based on the length of their sides and the measure of their angle. For Example- Equilateral Triangle ( A Trigion with all sides and angles equal), Isosceles triangle ( A trigon with 2 sides and angles equal), etc.

Quadrilateral Polygons- Quadrilateral Polygons is a polygon with 4 sides and 4 vertices. Quadrilateral Polygons are also called Quadrilaterals and Quadrangles. For Example- Square, Rhombus, etc.

Equilateral Polygons- Equilateral Polygons are polygons whose all sides tend to be equal. For Example- Equilateral Triangle, Square, Rhombus, etc.

Equiangular Polygons- Equiangular Polygons are figures with all interior angles equal. For Example- Rectangles, Squares, etc.

Pentagon Polygons- Pentagon polygon is the type of polygon with 5 sides and 5 vertices. Whenever all of the 5 edges of this polygon tend to be equal, then it is also called a regular pentagon.

Hexagon Polygons- Hexagon Polygons is a type of polygon where the shape has 6 sides and 6 vertices. A Regular Hexagon is a polygon that has 6 equal edges and all of its interior and exterior angles also measure equals.

Irregular Polygons- Irregular Polygons are polygons with no particular or unusual form. It represents that the general sides and angles for an Irregular polygon are unequal.

Tips to study Triangles

Triangle is a subtopic of polygons that contains a lot of formulas. To study and bring full marks in Triangles, the student can follow the given tips-

The student should make their own notes and charts of the formulas and properties of different triangles to understand them and use them later during exams.
Students should solve many questions about the topic. They can start by completing the Triangles NCERT Exercises
After completing NCERT, the student can move on to reference books like RD Sharma and RS Aggarwal. They can find solutions to these books at Vedantu's official website.
Students should also go through the previous year's exam papers and solve the Triangle's questions in them. This will help them to break the question pattern and understand the difficulty level of questions asked in an exam.
They can also find a lot of FREE resources like video lectures and a list of important questions that they can get from Vedantu's official website.
Students should practise Triangles seriously as the same topics revisit them in more co plex forms in higher classes.

These are some tips that a student can follow to understand the chapter triangles and get good marks.

FAQs on Triangle and It’s Properties

1. What is a Triangle?

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?

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 the 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 lengtthe h of other two sides.

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

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?

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 the as the relation between the legs and its angles. If the legs of right-angled triangles have same length, the angles the 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.

5. Why should one study topics like triangles in maths?

The investigation of math improves you at taking care of issues. It gives your abilities that you can use across different subjects and apply in various work jobs.

It creates abilities:

Association
Decisive reasoning.
Using time effectively.
Correspondence
Independent direction.
Information examination.

Significance of Mathematics: The significance of math should be visible in secret ways, and regular utilization, surrounding us: PCs, planes, body scanners, programming, coding, and gives clearness in critical thinking. Math gives clearness in critical thinking and "mathematicians have consistently perceived that critical thinking is vital to their discipline because without an issue there is no math. Math helps practically in each vocation.

A few vocations and occupations that benefit from a degree in arithmetic incorporate designers, software engineers, analysts, statisticians, math instructors, and even business directors. These vocations give off an impression of being unique, yet the one thing they share practically speaking is that every one of them requires a solid created range of math abilities. Concentrating on math permits you to comprehend the world better. Mathematics is a universal language. Science is the "widespread language," which means it is the one language on the planet that is all around comprehended across various societies, nations, and dialects. The basic number juggling of 2+2=4 is something similar all over the planet. So indeed, mathematics can open the secrets of the universe.