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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 $$QR$$.
1700067_1262018_ans_91d8c2d7c596495f98b22160094557c6.PNG

Mathematics

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