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Prove that line joining the mid …

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Prove that line joining the mid points of two sides of triangle is half to the third side by vector method.

Posted by Tanvi Agrawal 5 years, 7 months ago

CBSE > Class 12 > Mathematics

1 answers

Roshan Shukla 5 years, 7 months ago

Consider a triangle ABC with D and E as the midpoints of the sides AB and AC respectively. Now, AD=DB...... (1) AE=EC...... (2) Therefore, AE=1/2 AC...... (3) AD=1/2 AD....... (4) AC - AB = BC (Triangle rule of vector addition).......(5) AE - AD = DE (Triangle rule of vector ardition).......(6) From eq 3 and 4 eq 6 can be written as, 1/2 AC - 1/2 AB = DE AC - AB = 2DE......(7) On comparing eq 5 and 7 BC=2DE

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