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CBSE Class 9 Answered

In figure, ABCD is a trapezium in which side AB is parallel to DC and E is the midpoint of side AD. If F is a point of side BC such that the segment EF||DC, prove that EF= 1/2(AB+DC)  
Asked by naysa.tathgir | 16 Nov, 2018, 11:24: PM
answered-by-expert Expert Answer
Figure shows the trapezium ABCD.
 
AB || CD  (given)
 
E is mid point of AD (given)
 
EF || DC (given)
 
Let us join BD and let EF meets BD at G.
 
since EF || DC and AB || DC, we have EG || AB.
 
In Δ ABD, EG || AB and E is mid point of AD. Hence EG = (1/2)AB and BG = DG ................(1)
 
similarly we can say GF || DC.
 
in Δ BCD,  FG || CD and G is mid point of BD. Hence GF = (1/2)DC ..........................(2)
 
from (1) and (2), we have   EG+GF = EF = (1/2)(AB+DC)
Answered by Thiyagarajan K | 16 Nov, 2018, 11:59: PM

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