Altitudes

Table of Contents

• Altitudes of a Triangle
• Summary
• What’s Next?

In the previous segment, we learnt about the Medians of a triangle. In this segment, we will learn about Altitudes of a triangle.

What are Altitudes of a triangle?

• An Altitude of a triangle is a perpendicular from a vertex to the side opposite to it.
• A triangle has three altitudes and they meet at exactly one point. That is, the altitudes of a triangle are concurrent.
• This point of intersection is known as the Orthocentre of the triangle.

For example, consider triangle ABC.

The three vertices are A, B, and C. Here,

• • seg AE is perpendicular to side BC.
  • seg BF is perpendicular to side AC.
  • seg CD is perpendicular to side AB.

So, the three altitudes of triangle ABC are the segments AE, BF, and CD, corresponding to the bases of the triangle BC, AC, and AB respectively.

The altitudes AE, BF, and CD are concurrent at point O, which is the orthocentre of triangle ABC.

Summary