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Vector Algebra

Question
CBSEENMA12033955

Prove that the line joining the middle points of two sides of a triangle is parallel to the third side and is half of it.

Solution
Let D, E be mid-points of sides AB and AC of the ∆ ABC.
therefore          DE with rightwards arrow on top space equals space DA with rightwards arrow on top space plus space AE with rightwards arrow on top
[By Triangle Law of Vectors in increment thin space ADE]
                             equals space 1 half BA with rightwards arrow on top space plus space 1 half AC with rightwards arrow on top space equals space 1 half left parenthesis BA with rightwards arrow on top space plus space AC with rightwards arrow on top right parenthesis
therefore space space space DE with rightwards arrow on top space equals space 1 half space BC with rightwards arrow on top
therefore space space space space space space space DE thin space vertical line vertical line thin space BC space and space DE space equals space 1 half BC.

Hence the result.