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ICSE Class 9 Answered

ABCD is a quadrilateral in which AB is parallel to CD. P is the midpoint of BC.PQ is drawn parallel to CD which meets AD at Q.Prove that PQ bisects AD.
Asked by addhyadwipayan | 13 Jan, 2019, 10:36: PM
answered-by-expert Expert Answer
Figure shows a parallelogram ABCD. P is mid point of BC. PQ is drawn that is parallel to CD.
 
Let us join A and C. Let PQ intersect AC at O.
 
In ΔABC, PO is parallel to AB ( because it is given that PQ || CD and in parallelogram CD||AB )
Since P is mid point of BC, parallel line drawn through P bisect the other side AC.
 
Hence AO = OC.
 
Now in ΔACD , OQ is parallel to CD.
Line OQ which is parallel to CD and also passing through mid point O of AC,  bisects the other side AD.
 
Hence it is proved that, PQ bisects AD
Answered by Thiyagarajan K | 14 Jan, 2019, 10:58: AM

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