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
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