Question

5. Prove that a line joining the midpoints of any two sides of a triangle is parallel to the third
side. (Using converse of basic proportionality theorem)​

Answer 1

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Answer 2

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.