Question

in a trapezium ABCD AB||DC if P is the midpoint of AD then prove that the line drawn through P and parallel to AB bisects BC.
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Answer 1

Step-by-step explanation:

In triangle ADC,

P is midpoint of AD. (Given)

PR||DC (Given)

So,

R is midpoint of AC (By mid point theorem)

Now,

In triangle ACB,

R is midpoint of AC (proved above)

AB || RQ ( Given)

So,

Q is midpoint of BC ( By midpoint theorem)

Therefore,

BQ=QC

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