Mariya kaviya risshoni

  Geometry is an important part of mathematics that deals with different shapes and figures. Triangles are an important part of geometry and the mid-point theorem points towards mid points of the triangle. What is Mid-Point Theorem? This theorem states that”  The line segment joining mid-points of two sides of a   triangle is parallel to the third side of the   triangle and is half of it” Proof of Mid-Point Theorem A triangle ABC in which D is the mid-point of AB and E is the mid-point of AC. To Prove:  DE ∥ BC and DE = 1/2(BC) Construction Extend the line segment joining points D and E to F such that DE = EF and join CF. Proof In ∆AED and ∆CEF  DE = EF (construction) ∠1 = ∠2 (vertically opposite angles) AE = CE (E is the mid-point) △AED ≅ △CEF by SAS criteria Therefore,  ∠3 =∠4 (c.p.c.t) But these are alternate interior angles. So, AB ∥ CF AD = CF(c.p.c.t) But AD = DB (D is the mid-point) Therefore, BD = CF In BCFD BD∥ CF (as AB ∥ CF) BD = CF BCF...