Altitude of a triangle also known as the height of the triangle, is the perpendicular drawn from the vertex of the triangle to the opposite side.

**Altitude
of a Triangle**

Altitude
of a triangle also known as the height of the triangle, is the perpendicular drawn from the vertex of the triangle
to the opposite side.

The altitude
makes a right angle with the base of a triangle. Here, in ∆ABC, AD is one of the
altitudes as AD ⊥
BC.

** **

**Activity**

In the same way, you find altitudes of other two sides. Also, with
the help of your teacher, you find altitudes of right angled triangle and obtuse
angled triangle. Do the altitudes of triangle pass through the same point? What
is your conclusion? We see that,

**The three altitudes of
any triangle are concurrent.**

The point of concurrence is known as its Orthocentre, denoted by
the letter H.

** **

**Think**

**1. In any acute angled
triangle**, all three
altitudes are inside the triangle. Where will be the orthocentre?

In the interior of the triangle
or in its exterior?

**Solution: **Interior of the triangle.

Altitude of an acute triangle

**2. In any right angled
triangle,** the altitude
perpendicular to the hypotenuse is inside the triangle; the other two altitudes
are the legs of the triangle. Can you identify the orthocentre in this case?

**Solution:** Vertex containing 90°

Altitude of a right triangle

**3. In any obtuse angled
triangle**, the altitude
connected to the obtuse vertex is inside the triangle, and the two altitudes connected
to the acute vertices are outside the triangle. Can you identify the orthocentre
in this case?

**Solution:** Exterior of the triangle.

Altitude of an obtuse triangle

Tags : Geometry | Chapter 5 | 8th Maths , 8th Maths : Chapter 5 : Geometry

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8th Maths : Chapter 5 : Geometry : Altitude of a Triangle | Geometry | Chapter 5 | 8th Maths

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