**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.5 Question 6**

**6.** ABC is an equilateral triangle of side 2a. Find each of its altitudes.

**Solution:**

**Given: ** is equilateral with each side equal to **2a**. AF BC, BD AC and CE AB.

In and .

{ is equilateral, both are equal to 60 degrees}

{Each 90 degrees}

By, **AA similarity criterion**, ~

Therefore, we have ** (1)**

**{Corresponding sides of similar triangles are proportional}**

But ,we have AB = AC { is equilateral} **(2)**

Putting **(2)** in **(1)**, we get

We have BC = 2a. So, we get BF = a. **(3)**

In

Using Pythagoras theorem, we get

**{Pythagoras theorem states that in a right angled triangle, the square of hypotenuse is equal to the sum of squares of the other two sides}**

{Using **(3)**}

Similarly, we can prove that