Question

Let P and Q be the mid points of AB and AC respectively. Then PQ|| Bc such that PQ = 1/2 BC

Answer 1

Step-by-step explanation:

Mid point theorem

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Answer 2

Answer:Suppose the median AD intersects PQ at E.

Now,  PQ∣∣BC

⇒ ∠APE=∠B and ∠AQE=∠C

So, in △  

′

sAPE and ABD, we have

   ∠APE=∠ABD     and,

   ∠PAE=∠BAD              [Common]

∴ △APE∼△ABD

⇒  

BD

PE

​  

=  

AD

AE

​  

.........(i)

Similarly, we have

     △AQE∼△ACD

∴  

CD

QE

​  

=  

AD

AE

​  

.........(ii)

From (i) and (ii), we get

     

BD

PE

​  

=  

CD

QE

​  

 

⇒    

BD

PE

​  

=  

BD

QE

​  

        [∵ AD is the median ∴ BD=CD]

⇒  PE=QE

Hence, AD bisects PQ.