Basic Proportionality Theorem Class 10th (OR) B.P.T. or Thales Theorem Converse of basic proportionality theorem, thales theorem 10th standard, theorem 6.2 class 10 Statement:- If a line is drawn parallel to one side of the triangle to intersect the other two sides in two distinct points, the other two sides are divided in the same ratio. Given:- A Δ ABC in which line l ॥ BC, intersect side AB and AC at point D and E To Prove :- Construction :- Draw EM 丄 AB and DN 丄 AC. Also join BE and CD Proof :- Area of triangle = ✕ Base ✕ Height Area of △ ADE = ✕ AD ✕ EM ..............(1) Area of △ BDE = ✕ BD ✕ EM ..............(2) Divide equation (1) by equation (2) we get Similarly ΔBED and ΔCDE are two triangles on the same base and lie between the same parallel DE and BC ∴ Ar(ΔBED) = Ar(ΔCDE)...