Prove that any line parallel to parallel sides of a trapezium divides the non parallel sides proportionally.
Answers
Given : line parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally
To find : Prove
Solution:
Let say ABCD is a trapezium
AB || CD
PQ || AB || CD
intersecting AD at P & BC at Q
Join AC which intersect PQ at R
in Δ ABC RQ ║ AB as PQ || AB ( R is on PQ)
=> CR/AR = CQ/BQ
in Δ CDA PR ║ CD as PQ || CD ( R is on PQ)
=> AR/CR = AP/DP
=> CR/AR = DP/AP
CR/AR = CQ/BQ
CR/AR = DP/AP
=> CQ/BQ = DP/AP
Hence line parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally
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