Triangle and Its Properties Explained with Definitions 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:

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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

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.