if any straight line be drawn from the vertex of a triangle to its opposite side prove that it will be bisected by the straight line which joins the mid point of the opposite sides?
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ABC is a triangle, in which D is the mid - point of AB and E is the mid-point of AC. AL is a straight line that intersects DE at M and BC at L. TO PROVE : DE bisects AL.PROOF : Since D and E are the mid points of the sides AB and AC of △ ABC, then DE || BC .....(1) [Mid point theorem]Since DE || BC, then DM || BL. [as DM is a part of DE and BL is a part of BC].In triangle ABL, we have D is the mid point of AB and DM || BL , thenM must be the mid point of AL. [Converse of mid point theorem]⇒ AM = ML⇒ DE bisects AL Hope this information will clear your doubts about Triangles.
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