Question

Prove that in a triangle if the square of one side is equal to the sum of the

squares of the remaining two sides, then the triangle is a right angled triangle​

Answer 1

Answer:

ANSWER

Given:- ABC is a triangle

AC

2

=AB

2

+BC

2

To prove:- ∠B=90°

Construction:- Construct a triangle PQR right angled at Q such that, PQ=AB and QR=BC

Proof:-

In △PQR

PR

2

=PQ

2

+QR

2

(By pythagoras theorem)

⇒PR

2

=AB

2

+BC

2

.....(1)(∵AB=PQ and QR=BC)

AC

2

=AB

2

+BC

2

.....(2)(Given)

From equation (1)&(2), we have

AC

2

=PR

2

⇒AC=PR.....(3)

Now, in △ABC and △PQR

AB=PQ

BC=QR

AC=PR(From (3))

∴△ABC≅△PQR(By SSS congruency)

Therefore, by C.P.C.T.,

∠B=∠Q

∵∠Q=90°

∴∠B=90°

Hence proved.

Answer 2

Answer:

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