The Triangle and its Properties

Basics of Triangles

Triangles!!! The word comes from an old Latin word “triangulum” which means three-cornered. Triangles are basic shapes that we come across in our day to day life. You are surrounded by them. The slice of pizza, the hill nearby, the roof of your house are all triangles if you look at their 2-dimensional pictures. What are they and where do we see them? Let us now study the basics of triangles.

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A triangle is a simple closed curve or polygon which is created by three line-segments. In geometry, any three points, specifically non-collinear, form a unique triangle and separately, a unique plane (known as two-dimensional Euclidean space). The basic elements of the triangle are sides, angles, and vertices.

Basics of Triangle

Some Basics of Triangles

Let us now explore some basics of triangles to have a better understanding of the geometry of it. We will first look at the two ways we can classify triangles. The first type of classification is done on the base of the angles of the triangle. The classifications are as follows:

  • Acute Triangle: This is a triangle in which each of the angles is acute and measure is less than 90°
  • Right Angled Triangle: It is a form of a triangle wherein one particular angle is a right angle
  • Obtuse Triangle: Triangle in which one of the angles stays obtuse is called an obtuse triangle.

Further, triangles can be classified depending on the number of congruent sides that means the side length. The classification is as follows:

  • Scalene Triangle: meaning that every side length in a triangle is different.
  • Equilateral Triangle: means that every side length in a triangle is similar.
  • Isosceles Triangle: means, at least two of the triangle side lengths are similar.

Important Properties of Triangles

  • We know that the sum of the measures of the three angles of a triangle is always 180°. Also, the sum of the lengths of any two sides of a triangle is always greater than the length of the third side of the triangle. In the same way, the difference between the lengths of any two sides of a triangle is less than the length of the third side of the triangle.
  • In a triangle, the medians is a line segment joining a vertex of the triangle to the midpoint of the opposite side.

Basics of Triangles

  • So here in this triangle, then AE is the median. Also by taking the midpoint of AB as D, we join CD so CD is also a median, and as midpoint AC is F, we take FB as the median. So these are the three medians of the triangle.  The three medians of the triangle are concurrent and their point of concurrence is called the centroid of the triangle.
  • The altitude has one endpoint at a vertex of the triangle and other on the line containing the opposite side. The altitudes of the triangle are concurrent and their point of concurrence is called the orthocentre of the triangle.
  • Area of the triangle is calculated by the formula: Area = \( \frac{1}{2} \) × base × height

Browse more Topics under The Triangle And Its Properties

Solved Questions

Q1. How many triangles can be drawn having its angles as 53° 64° and 63°?

  1. 1
  2. 2
  3. None
  4. More than 2

Solution: D. The three angles given are 53° 64° and 63°
So the sum of the angles is 53 + 64 + 63 =  180°
Sum of the angles of triangles is always 180°
Hence many angles can be formed with these three angles.

Q2. In a triangle ABC,  ∠B = ∠C = 45°  then the triangle is ……………………

  1. right-angled triangle
  2. acute-angled triangle
  3. obtuse-angled triangle
  4. equilateral triangle

Solution: A. In ΔABC,
∠A + ∠B + ∠C = 180° Sum of all interior angles of a triangle is 180°.
∠A + 45° + 45° = 180° [ ∠B + ∠C = 45°] given
As one of the angles is 90°
∴ It is a right-angled triangle.

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