Question

prove that A line joining the mid points of any two sides of traingle is parallel to the third side​

Answer 1

Step-by-step explanation:

Given: Let us assume ΔABC where D is the mid point of AB and E is the mid point of AC.

To prove: DE||BC

Proof:

In ΔABC,

D is the mid point of AB

⇒ AD=DB

⇒AD/DB=1 ……………..(1)

E is the mid point of AC

⇒AE=EC

⇒AE/EC=1 ……………(2)

From (1) & (2)

AD/DB=AE/EC

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

∴DE||BC.

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