CBSE Class 10-Mathematics: Chapter – 6 Triangles Part 20 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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.

Find the Measure of ∠ PKR in Figure

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

∆ DEF is a Right Angled Triangle

Hence, is a right triangle.

In

Now in

is right-angled at K