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CBSE Class 10 - Mathematics: Chapter β 6 Triangles Part 20
Question 5:
In a triangle if the square of one side is equal to the sum of the squares on the other two sides. Prove that the angle apposite to the first side is a right angle. Use the above theorem to find the measure of in figure given below.
Answer:
Given: such that
To prove: Triangle ABC is right angled at B
Construction: Construct a triangle DEF such that
Proof: is a right-angled triangle right angled at
By Pythagoras theorem, we have
Thus, in , we have
Hence, is a right triangle.
In
Now in
is right-angled at K