Question

a triangle if the Square of one side
is equal to the sum of the square of the remaining two sides then the triangle is a right angled triangle​

Answer 1

Step-by-step explanation:

ABC is a triangle

ABC is a triangleAC² =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 = PQ² + QR²

.

.....(1)(∵AB=PQ and QR=BC) (figure)

AC² =AB² + BC²

.....(2)(Given)

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

AC² = PR²

so

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

∠B=∠Q∵∠Q=90°

∠B=∠Q∵∠Q=90°∴∠B=90°

Hence proved.