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In the following diagram, lines l, m and n are parallel to each other. Two transversals p and q intersect the parallel lines at points A, B, C and P, Q, R as shown.

Prove that: ABBC=PQQR\dfrac{AB}{BC} = \dfrac{PQ}{QR}

In the diagram, lines l, m and n are parallel to each other. Two transversals p and q intersect the parallel lines at points A, B, C and P, Q, R as shown. Prove that: AB/BC = PQ/QR. Similarity, Concise Mathematics Solutions ICSE Class 10.

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Join A and R. Let AR meet BQ at point D.

In the diagram, lines l, m and n are parallel to each other. Two transversals p and q intersect the parallel lines at points A, B, C and P, Q, R as shown. Prove that: AB/BC = PQ/QR. Similarity, Concise Mathematics Solutions ICSE Class 10.

In ∆ACR, BD || CR.

By Basic proportionality theorem, we get

ABBC=ADDR\dfrac{AB}{BC} = \dfrac{AD}{DR} …..(1)

In ∆APR, DQ || AP.

By Basic proportionality theorem, we get

PQQR=ADDR\dfrac{PQ}{QR} = \dfrac{AD}{DR} …..(2)

From (1) and (2) we get :

ABBC=PQQR\dfrac{AB}{BC} = \dfrac{PQ}{QR}

Hence proved that ABBC=PQQR\dfrac{AB}{BC} = \dfrac{PQ}{QR}.

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