Question

In a triangle if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite to the first side is a right angle. Prove

Answer 1

Answer:

MATHS

In a triangle, if the square of one side is equal to the sum of the squares of other two sides, then the angle opposite to the first side is a right angle. Prove it

October 15, 2019Aamina Akavaram

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ANSWER

Given:- ABC is a triangle

AC2=AB2+BC2

To prove:- ∠B=90°

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

Proof:-

In △PQR

PR2=PQ2+QR2(By pythagoras theorem)

⇒PR2=AB2+BC2.....(1)(∵AB=PQ and QR=BC)

AC2=AB2+BC2.....(2)(Given)

From equation (1)&(2), we have

AC2=PR2

⇒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

∵