CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.5 Question 15
15. In an equilateral triangle ABC, D is a point on side BC such that
. Prove that
.
Solution:
Given:
is equilateral. D is the point on BC such that
To Prove:
Construction: Draw AE
BC
Proof:
In
(1)
But, we have AB = AC {ABC is an equilateral triangle} (2)
Putting (2) in (1), we get
We have,
{By, Pythagoras Theorem}
{CE = BE, In equilateral triangle altitude is also the median}
{
}
(3)
But, we have AB = BC {ABC is an equilateral triangle}
Putting this in (3), we get
Hence Proved
Annu says
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