In the adjoining figure, ABCD is a trapezium in which AB||DC and P, Q are the midpoints of AD and BC respectively. DQ and AB when produced meet at E. Also, AC and PQ intersect at R. Prove that (i) DQ = QE, (ii) PR||AB and (iii) AR = RC.

Explanation

`triangle QCD ~=triangle QBE. " So, " DQ = QE.`
PQ||AE `rArr ` PQ||AB||DC||`rArr` AB||PR||DC.
Now, AB||PR||DC are cut by AD and AC. Use intercept theorem.