Question

# $$A$$ and $$B$$ are respectively the points on the sides $$PQ$$ and $$PR$$ of a triangle $$PQR$$ such that $$PQ = 12.5\ cm, PA = 5\ cm, BR = 6\ cm$$ and $$PB = 4\ cm$$. Is $$AB \parallel QR$$? Give reasons for your answer.

Solution

## From the dimensions given in the question,Consider the $$\triangle PQR$$So, $$PQ/PA = 12.5/5$$$$= 2.5/1$$$$PR/PB = (PB + BR)/PB$$$$= (4 + 6)/4$$$$= 10/4$$$$= 2.5$$By comparing both the results,$$2.5 = 2.5$$Therefore, $$PQ/PA = PR/PB$$So, $$AB$$ is parallel to $$QR$$.Mathematics

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