Question

theorem of converse of pythagoras


have 50 points in ur pocket

Answer 1

ACCORDING TO PYTHAGORAS THEOREM,
=>In an right-angled triangle,the square of hypotenuse is equals to the sum of squares of other two sides.
(HYPOTENUSE)^2 = (BASE)^2 + (PERPENDICULAR)^2

CONVERSE:-
The converse of the Pythagorean Theorem is:

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

That is, in ΔABCΔABC, if c2=a2+b2c2=a2+b2 then ∠C∠Cis a right triangle, ΔPQRΔPQR being the right angle.



We can prove this by contradiction.

Let us assume that c2=a2+b2c2=a2+b2 in ΔABCΔABCand the triangle is not a right triangle.

Now consider another triangle ΔPQRΔPQR. We construct ΔPQRΔPQR so that PR=aPR=a, QR=bQR=b and ∠R∠R is a right angle.



By the Pythagorean Theorem, (PQ)2=a2+b2(PQ)2=a2+b2.

But we know that a2+b2=c2a2+b2=c2 and a2+b2=c2a2+b2=c2 and c=ABc=AB.

So, (PQ)2=a2+b2=(AB)2(PQ)2=a2+b2=(AB)2.

That is, (PQ)2=(AB)2(PQ)2=(AB)2.

Since PQPQ and ABAB are lengths of sides, we can take positive square roots.

PQ=ABPQ=AB

That is, all the three sides of ΔPQRΔPQR are congruent to the three sides of ΔABCΔABC. So, the two triangles are congruent by the Side-Side-Side Congruence Property.

Since ΔABCΔABC is congruent to ΔPQRΔPQR and ΔPQRΔPQR is a right triangle, ΔABCΔABC must also be a right triangle.

This is a contradiction. Therefore, our assumption must be wrong.

HOPE IT WILL HELP YOU AND THANKS FOR THE POINTS.

Answer 2

Heya mate
The answer is here in the pic




hope it helps you