Question

In a trapezium abcd ab and dc are the parallel sides .E is the mid point of ad and f is mid point of bc then prove that:ab+dc=2ef

Answer 1

Given:ABCD IS A TRAPEZIUM WITH AB //s TO DC AND E &F ARE MIDPOINTS OF AD & BC.
TO PROVE:AB+DC=2EF
CONSTRUCTION:JOIN AC
PROOF:NOW AS AB //S TO DC
SO AB //DC//EF
NOW,IN TRIANGLE ADC
E IS MIDPOINT OF AD & EF// TO DC
SO BY CONVERSE MIDPOINT TH^m LINE DRAWN FROM E // TO DC LET THAT LINE be EP AND EQUAL TO 1/2DC
=》EP // DC & EP =1/2DC--(1)
SIMILARLY,WE CAN PROVE THAT
IN TRIANGLE ABC
LINE F // TO AB LET THAT LINE BE FQ AND
EQUAL TO 1/2 AB
=》FQ//AB & FQ = 1/2AB --(2)
BY ADDING EQ.(1)&(2)
WE GET, EP +FQ=1/2(DC+AB)
=》EF=1/2(DC+AB)
=》2EF=DC + AB
=》AB+DC=2EF
HENCE,PROOVED

Answer 2

Step-by-step explanation:

$ef = \frac{1}{2} (ab + dc) \\ = > ab + dc = 2ef$

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