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Chapter 6 – The Triangle and its Properties

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

A polygon with three sides is called a triangle (tri = three). It is a closed structure with three sides, three vertices, and three angles. The triangles and their properties help to distinguish them into different types. It includes the sum of interior angles, and angle sum property of a triangle. There are many types of triangles, however, two special triangles: equilateral and isosceles, show the properties mentioned above but vary in the sides.

Take a plain paper and cut a triangle out of it. Try to fold this triangle into two equal parts; you will see a line connecting the two vertices. This is called the median of a triangle. A median connects a vertex of a triangle to the midpoint of the opposite side. It helps to study the triangle and its properties.

Cut a triangle from a hardboard and place it on your table. The height of the triangle from its tip to the base is called the altitude of a triangle. Altitude is perpendicular to the base of the triangle. So, one endpoint of altitude is at the vertex of the triangle, and another on the opposite side.

Take a look at ΔABC (in the figure). The angle located on the outside of the triangle is called the exterior angle of a triangle. And the angles inside the triangle are called interior angles of the triangle. The exterior angle of a triangle is equal to the sum of its opposite interior angles. This is also called the exterior angle property of a triangle.

Source: Class 7 Maths NCERT

For example:

∠ACD = Exterior angle of a triangle

∠BAC and ∠ABC = Interior angles of the triangle

From the exterior angle property of a triangle, ∠ACD = ∠BAC + ∠ABC

Suppose, we cut a triangle on paper and measure all the interior angles. We tear the triangle into three parts, each carrying one angle. If you rearrange the pieces and calculate the sum of the angles, what do you observe? Before and after tearing the triangle, the sum of all the interior angles is 180°.

According to the Angle Sum Property of a Triangle, the total measure of the three angles of a triangle is 180°.

With the help of a scale, draw a triangle having all equal sides. Such a triangle will be termed an equilateral triangle, where each angle measures 60°.

Source: Class 7 Maths NCERT

Draw another triangle with two sides that are equal and the third side unequal. Such a triangle is called an isosceles triangle. In an isosceles triangle, base angles opposite to the equal sides are equal.

Source: Class 7 Maths NCERT

Draw a triangle randomly without an exact measurement of the sides. Now measure each side and find the sum of any two sides. What did you get? You will observe that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. Now, try to subtract the length of any two sides. You will observe that the difference between the lengths of any two sides is smaller than the length of the third side.

Draw a triangle with one right angle, i.e., 90 degree. Such a triangle will be termed a right-angled triangle. In this diagram, the right angle is ∠ABC.

Source: Class 7 Maths NCERT

In a right-angled triangle, the side opposite to the right angle is called the hypotenuse (in the figure, AC), and the other two sides are called its legs (here, AB and AC). All the right-angled triangles show Pythagoras property. If the triangle isn’t the right angle, this property isn’t valid. Hence, you can check whether it is a right-angled triangle or not.

According to Pythagoras property:

The square on the hypotenuse = the sum of the squares on its legs

AC² = AB² + BC²

All the triangles (acute, obtuse, or right-angled, equilateral, isosceles, or scalene) are polygons with an altitude and median. The Triangle and its Properties are highly specific, including angle sum property and exterior angle property. The Pythagoras property is exclusive to right-angled triangles.

  1. What are a triangle and its properties?
    A triangle is a polygon with three sides, three angles, and three vertices. The properties of triangles are:
    a) The sum of all internal angles of a triangle is equal to 180 degree.
    b) The exterior angle of the triangle is equal to the sum of its interior opposite angles.
  2. What are the three properties of a triangle?
    a) The sum of all internal angles of a triangle is equal to 180 degree, i.e., angle sum property.
    b) The exterior angle of the triangle is equal to the sum of its interior opposite angles, i.e., exterior angle property.
    c) The sum of the lengths of any two sides of a triangle is always greater than the third side’s length. 
  3. What is triangle in class 7?
    A triangle is a simple closed curve made of three line segments.
     
  4. What are the properties of right-angle triangles?
    a) A right-angle triangle has one angle called a right angle, i.e., 90 degree.
    b) The side opposite to the right angle is called the hypotenuse, which is the longest side.
    c) The other two sides adjacent to the hypotenuse are called Base and Perpendicular.
    d) The sum of the remaining two interior angles is equal to 90 degree.
  5. What are the seven types of triangles?
    Triangles can be classified based on sides and angles. The seven types of triangles are:

    1. Equilateral 
    2. Acute-angled isosceles 
    3. Obtuse-angled isosceles 
    4. Right-angled isosceles 
    5. Acute-angled scalene
    6. Obtuse-angled scalene
    7. Right scalene triangle

For more information about the triangle and its properties, check out MSVgo, a video library with lectures and animated videos. It has been developed to help students embark on conceptual learning among students from grades 6-12 for the CBSE, ICSE, ISC, IGCSE, and IB curriculum.

High School Physics

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Middle School Math

  • Addition
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