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 points of the opposite sides.

Question

Surbhi · Answer

Given in triangle ABC, a straight line AG is drawn through the vertex A .E and F are respectively mid points of sides AB and AC .It is joined intersecting the line AG at O.Now ,in triangle ABC ,EF =1/2BC and EF||BC (by mid point theorem) (1).Now in triangle AGC ,F is mid point and OF is parallel to GC from equation 1.hence O is mid point of AG( by converse of mid point theorem.Hence AG is biscte by EF

Samar pratap · Answer

Please follow the solution to the above given query:GIVEN : ​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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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 points of the opposite sides.

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 points of the opposite sides.

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