CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.5 Question 5
5. ABC is an isosceles triangle with AC = BC. If,
, prove that ABC is a right triangle.
Solution:
Given: ABC is an isosceles triangle with
.
To Prove:
is a right angled triangle.
Proof: It is given that ABC is an isosceles triangle with
. It means AB is the biggest side of triangle. Hence, we have BC = AC. (1)
.
(2)
Putting (1) in (2), we get
Therefore, by converse of pythagoras theorem,
is right angled at C.
{In a triangle, if square of one side is equal to sum of squares of other two sides then the given triangle is right angled}
Hence Proved
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