Question

ABCD is a trapezium in which AB and CD are parallel. Prove by vector methods that the mid points of the sides AB,CD and the intersection of the diagonals are collinear

Answer 1

Answer:

By converse of mid-point theorem, we know that a line drawn through the mid-point of any side of a triangle and parallel to another side, bisects the third side.

In ΔABD,

EF || AB and E is the mid-point of AD.

Therefore, G will be the mid-point of DB.

As EF || AB and AB || CD,

∴ EF || CD (Two lines parallel to the same line are parallel to each other)

In ΔBCD, GF || CD and G is the mid-point of line BD. Therefore, by using converse of mid-point theorem, F is the mid-point of BC.

Step-by-step explanation:

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