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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?

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Answers (1)

Answer : [True]

Given: PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm

QA = QP – PA = 12.5 – 5 = 7.5 cm

\frac{PA}{AQ}=\frac{5}{7.5}=\frac{50}{75}=\frac{2}{3}

\frac{PB}{PR}=\frac{4}{6}=\frac{2}{3}

Here

\frac{PA}{AQ}=\frac{PB}{PR}

According to Converse of basic proportionality theorem if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

\therefore AB\parallel QR

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