Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Let ABC be the triangle, D be the mid-point AB and E be the mid-point of AC. So, in △ ABC, .........(1) .........(2) From (1) and (2), we get : . By theorem 6.2, If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. Since, In △ ABC, . ∴ DE || BC. Hence, proved that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

In figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

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Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

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Mathematics

Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Triangles

Related Questions

In figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.