Tuesday, 1 August 2017

Triangles VII - List of properties of Right Angled Triangle

In this post, we will discuss Properties of Right Angled Triangle to solve geometric questions asked in SSC Exams.


Right Angled Triangle

A right angled triangle is a triangle which contains one 90° angle. There are some properties related to right angled triangle and many SSC aspirants have doubts about these. In this post, we will discuss all the properties of right angled triangle that will help you solve geometric questions asked on them. 

In our previous posts, we have discussed different types of triangles, properties of triangles and different centres of a triangle - Centroid, Circumcentre, Orthocentre and Incentre. Brush up on the basics before we begin.


What is a Right-Angled Triangle 

A right angled triangle is a triangle which contains one 90° angle.
In any triangle, the side opposite to the larger angle is the largest side of a triangle. 

In right-triangled ABC, 
AB is the side
BC is the base 
AC is the hypotenuse 

Right Angled Triangle

Pythagoras Theorem  

Pythagoras Theorem states that the square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides.

In right-angled triangle ABC, 

Right Angled Triangle

Properties of right angled triangle when a perpendicular is drawn on the hypotenuse.


Right Angled Triangle

When a perpendicular is drawn on the hypotenuse the triangle is divided into two parts, i.e., Triangle ADB and Triangle BDC. 

Triangle ADB is similar to the Triangle BDC. Hence on the basis of similarity, corresponding angles are equal. 


Right Angled Triangle

In similar triangles, corresponding sides are in proportion. 


Right Angled Triangle

Hence, when we take,
Right Angled Triangle

We get,
BD2 = AD x DC
AB2 = AC x AD
BC2 = AC x DC

Another property of right angled triangle is 

Right Angled Triangle

We hope this list of properties of right angled triangle has helped you learn all the properties of right angled triangle. Do write in the comment section below on how this post has helped you understand properties of right angled triangle. To practice questions on right angled triangle, download the questions for practice. 

Stay tuned for the next post. 
Right Angled Triangle
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