Wednesday, 26 July 2017

Triangles IV: What is Orthocenter of a Triangle?

In this post, we will discuss all the properties related to orthocenter of a triangle which will help us solve geometric questions in SSC CGL Exams.

Orthocenter of a Triangle

What is Orthocenter? Many aspirants who attempt SSC Exams have this question and they often fail to understand the concept and skip geometric questions that are asked on orthocenter of a triangle. In this post, we will discuss all the properties of orthocenter of a triangle which will help you solve geometric questions and hence help you crack SSC Exams easily. 

In our previous post, we have discussed the centroid of a triangle. In this post, we will discuss another centre of a triangle named orthocenter of a triangle. 

Before moving further let's understand the most important term related to orthocentre of a triangle - Altitude.

What is an Altitude of a triangle? 

Altitude of a triangle is a perpendicular which is drawn from the vertex of a triangle to the opposite side of a triangle. 
                                                           AD is the Altitude

Orthocenter of a Triangle

In a triangle, there are only three altitudes that can be drawn. AD, CF, and BE are the Altitudes of the triangle given below.

Orthocenter of a Triangle

What is orthocenter of a triangle? 

Orthocenter of a triangle is the point of intersection where all the three altitudes of a triangle intersect.

Orthocenter is denoted by the letter "H."

Orthocenter of a Triangle

Position of the Orthocenter of a Triangle for different types of triangles:

Based on the type of a triangle, the position of the orthocenter changes.

1. Acute Angled Triangle: In an acute angled triangle, the orthocenter of the triangle lies inside the triangle. 

Orthocenter of a Triangle

2. Obtuse Angled Triangle: In an obtuse angled triangle, the orthocenter of the triangle lies outside the triangle. 

Orthocenter of a Triangle

3. Right Angled Triangle: In a right angled triangle, the orthocenter of the triangle lies on the vertex of the triangle.

Orthocenter of a Triangle

The angle made by any side with the orthocenter of a triangle and the vertical angles are supplementary


Orthocenter of a Triangle

1. Angle BHC + Angle A = 180 degrees 
2. Angle AHC + Angle B = 180 degrees 
3. Angle AHB + Angle C = 180 degrees 

Hope it's now easier for you to attempt questions that are based on the orthocentre of a triangle.

Do write in the comments section below on how this post has helped you understand the properties of Orthocentre of a triangle asked in mock tests for SSC CGL. Also, download free questionnaire for practice!


Stay tuned for our next blog.

Orthocenter of a Triangle

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