Post Summarization: ● Thales Theorem and its proof. What is Thales's Theorem? If a straight line is drawn parallel to a side of a triangle, then it divides the other two sides proportionally. Given data, In ∆ABC, DE || BC Aim to prove: AD/DB = AE/EC First of all, join 'D' with 'C' and 'E' with 'B' with straight lines. Next, draw 'EL' perpendicular (90°) to 'AB' and 'DN' perpendicular (90°) to 'AC'. Now, as 'EL' is perpendicular (90°) to 'AB', therefore, 'EL' is the height of ∆AEL and ∆DEL. Again, ∆DEL and ∆BDE have a common apex point 'E', and the base of both triangles are on the same plane, Therefore, 'EL' is the height of ∆BDE. Similarly, 'DN' is the height of ∆CDE. As we know, the area of a triangle = 1/2×b×h Where, b = Base of the triangle, and h = Height of triangle. Therefore, AREA of ∆ADE / AREA of ∆BDE = (1/2×AD×EL) / (1/2×DB×EL) = AD / DB ................