Yo ladies and gentlemen :p....provide me the proof of Converse of Pyth

1.	Yo ladies and gentlemen :p....provide me the proof of Converse of Pythagoras theorem ^^" with its statement ❤️
Answer» $\huge\underline\mathfrak\purple{Statement}$ In a triangle, if the square of one SIDE is equal to the sum of square of other two sides then prove that the triangle is right angled triangle. ________________________ $\huge\underline\mathfrak\purple{Solution}$ Given : AC² = AB² + BC² To prove : ABC is a right angled triangle. Construction : Draw a right angled triangle PQR such that, angle Q = 90°, AB = PQ, BC = QR. Proof : In triangle PQR, Angle Q = 90° ( by construction ) Also, PR² = PQ² + QR² ( By using PYTHAGORAS theorem )...(1) But, AC² = AB² + BC² ( Given ) Also, AB = PQ and BC = QR ( by construction ) THEREFORE, AC² = PQ²+ QR²....(2) From EQ (1) and (2), PR² = AC² So, PR = AC Now, In ∆ABC and ∆PQR, AB = PQ ( By construction ) BC = QR ( By construction ) AC = PR ( Proved above ) Hence, ∆ABC is congruent to ∆PQR by SSS criteria. Therefore, Angle B = Angle Q ( By CPCT ) But, Angle Q = 90° ( By construction ) Therefore, Angle B = 90° Thus, ABC is a right angled triangle with Angle B = 90° ____________________ Hence proved!

Yo ladies and gentlemen :p....provide me the proof of Converse of Pythagoras theorem ^^" with its statement ❤️

Answer»

$\huge\underline\mathfrak\purple{Statement}$

In a triangle, if the square of one SIDE is equal to the sum of square of other two sides then prove that the triangle is right angled triangle.

________________________

$\huge\underline\mathfrak\purple{Solution}$

Given : AC² = AB² + BC²

To prove : ABC is a right angled triangle.

Construction : Draw a right angled triangle PQR such that, angle Q = 90°, AB = PQ, BC = QR.

Proof : In triangle PQR,

Angle Q = 90° ( by construction )

Also,

PR² = PQ² + QR² ( By using PYTHAGORAS theorem )...(1)

But,

AC² = AB² + BC² ( Given )

Also, AB = PQ and BC = QR ( by construction )

AC² = PQ²+ QR²....(2)

From EQ (1) and (2),

PR² = AC²

So, PR = AC

Now,

In ∆ABC and ∆PQR,

AB = PQ ( By construction )

BC = QR ( By construction )

AC = PR ( Proved above )

Hence,

∆ABC is congruent to ∆PQR by SSS criteria.

Therefore, Angle B = Angle Q ( By CPCT )

But,

Angle Q = 90° ( By construction )

Therefore,

Angle B = 90°

Thus, ABC is a right angled triangle with Angle B = 90°

____________________

Hence proved!