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03/06/2021 12:00 pm
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Using Converse of basic proportionality theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.
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03/06/2021 12:04 pm
Given, in ΔABC, D and E are the mid points of AB and AC respectively, such that,
AD = BD and AE = EC.
We have to prove that, DE || BC.
Since, D is the midpoint of AB
∴ AD=DB
⇒ AD/BD = 1 ……………….. (i)
Also given, E is the mid-point of AC.
∴ AE = EC
⇒ AE/EC = 1
From equation (i) and (ii), we get,
AD/BD = AE/EC
By converse of Basic Proportionality Theorem,
DE || BC
Hence, proved.