Question

Prove that any line parallel to the parallel sides of a trapezium divides the non-parallel sides
proportionally

Answer 1

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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