Question

what is thales theroem prove

Answer 1

Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem, and is mentioned and proved as part of the 31st proposition, in the third book of Euclid's Elements.[1] It is generally attributed to Thales of Miletus, who is said to have offered an ox (probably to the god Apollo) as a sacrifice of thanksgiving for the discovery, but sometimes it is attributed to Pythagoras.

Since OA = OB = OC, ∆OBA and ∆OBC are isosceles triangles, and by the equality of the base angles of an isosceles triangle, ∠OBC = ∠OCB and ∠BAO = ∠ABO.

Let α = ∠BAO and β = ∠OBC. The three internal angles of the ∆ABC triangle are α, (α + β), and β. Since the sum of the angles of a triangle is equal to 180°, we have

{\displaystyle \alpha +\left(\alpha +\beta \right)+\beta =180^{\circ }}{\displaystyle {2}\alpha +{2}\beta =180^{\circ }}{\displaystyle {2}(\alpha +\beta )=180^{\circ }}{\displaystyle \therefore \alpha +\beta =90^{\circ }.}

Answer 2

Hope this will help u...
Basic Proportionality Theorem(BPT) or Thales Theorem both are same .