If D, E and F are mid-points of the sides BC, CA and AB respectively of a △ABC, prove that AD and FE bisect each other.
Mid-point Theorem
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Question

If D, E and F are mid-points of the sides BC, CA and AB respectively of a △ABC, prove that AD and FE bisect each other.

KnowledgeBoat · Accepted Answer

△ABC with D, E and F as mid-points of the sides BC, CA and AB is shown below: D and E are midpoints of BC and CA respectively, DE = AB and DE || AB or DE || AF .......(1) Since, F is midpoint of AB, AF = AB ∴ AF = DE .......(2) F and D are midpoints of AB and BC respectively, FD = AC and FD || AC or FD || AE .......(3) Since, E is midpoint of AC, AE = AC ∴ FD = AE .......(4) From 1, 2, 3 and 4 we get, DE || AF, AF = DE and FD || AE, FD = AE. Hence, AEDF is a parallelogram. ∴ AD and EF bisect each other. Hence, AD and EF bisect each other.

Mathematics

If D, E and F are mid-points of the sides BC, CA and AB respectively of a △ABC, prove that AD and FE bisect each other.

Mid-point Theorem

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