Question

prove the Pythagorean formula, i will give brainliest, any maths genius ??s

Answer 1

Bhaskara began with a right triangle and then he drew an altitude on the hypotenuse. From here, he used the properties of similarity to prove the theorem.



Now prove that triangles ABC and CBE are similar.
It follows from the AA postulate that triangle ABC is similar to triangle CBE, since angle B is congruent to angle B and angle C is congruent to angle E. Thus, since internal ratios are equal s/a=a/c.
Multiplying both sides by ac we get
sc=a^2.

Now show that triangles ABC and ACE are similar.
As before, it follows from the AA postulate that these two triangles are similar. Angle A is congruent to angle A and angle C is congruent to angle E. Thus, r/b=b/c. Multiplying both sides by bc we get
rc=b^2.

Now when we add the two results we get
sc + rc = a^2 + b^2.
c(s+r) = a^2 + b^2
c^2 = a^2 + b^2,
concluding the proof of the Pythagorean Theorem.

Answer 2

Pythagoras formula can be proved by more than 200 ways
Earlier Pythagoras prove it by by drawing square around the side of triangle and proving that the area of hypotenuse square is equal to the sum of area of other two squares

but my favourite prove given by Einstein
using the the similarity method
Einstein draw a line in the right angle triangle touching the hypotenuse at right angles
by using the two right angle triangle he proved the Pythagoras theorem