Bpt proof class 10

Step -1: Stating Thales theorem . Thales theorem states that, If A, B and C are three distinct points on a circle, and if the line segment joining A and B forms a diameter of the circle, then ∠ ACB = 90 ∘ Step -2: Proving the theorem . To prove, ∠ ACB = 90 ∘ In △ AOC, AO = OC (radius of circle) ⇒ ∠ CAO = ∠ ACO In △ BOC, BO = OC (radius of circle) ⇒ ∠ CBO = ∠ BCO We can see that, ∠ ACB = ∠ ACO + ∠ BCO Now, ∠ ACB + ∠ CBA + ∠ BAC = 180 ∘ (angle sum property of triangle) ⇒ ∠ ACB + ∠ ACB = 180 ∘ ⇒ 2 ∠ ACB = 180 ∘ ⇒ ∠ ACB = 90 ∘ Hence proved .

Step -1: Stating Thales theorem . Thales theorem states that, If A, B and C are three distinct points on a circle, and if the line segment joining A and B forms a diameter of the circle, then ∠ ACB = 90 ∘ Step -2: Proving the theorem . To prove, ∠ ACB = 90 ∘ In △ AOC, AO = OC (radius of circle) ⇒ ∠ CAO = ∠ ACO In △ BOC, BO = OC (radius of circle) ⇒ ∠ CBO = ∠ BCO We can see that, ∠ ACB = ∠ ACO + ∠ BCO Now, ∠ ACB + ∠ CBA + ∠ BAC = 180 ∘ (angle sum property of triangle) ⇒ ∠ ACB + ∠ ACB = 180 ∘ ⇒ 2 ∠ ACB = 180 ∘ ⇒ ∠ ACB = 90 ∘ Hence proved .