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प्रश्न
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 || QR? Give reasons for your answer.
उत्तर
Given,
PQ = 12.5 cm,
PA = 5 cm,
BR = 6 cm
And PB = 4 cm
Then, QA = QP – PA
= 12.5 – 5
= 7.5 cm
Now, `("PA")/("AQ")`
= `5/7.5`
= `50/75`
= `2/3` ...(i)
And `("PB")/("BR")`
= `4/6`
= `2/3` ...(ii)
From equations (i) and (ii),
`("PA")/("AQ") = ("PB")/("BR")`
By converse of basic proportionally theorem,
AB || QR
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