A and B are mid points of PQ and RS of parallelogram PQRS. show that the line segments AS and BQ triseet the diagonal PR...
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ABCD is ∥gm
AB∥CD
AE∥FC
⇒AB=CD
1/2 AB= 1/2CD
AE=EC
AECF is ∥gm
In △DQC
F is mid point of DC
FP∥CQ
By converse of mid point theorem P is mid point of DQ
⇒DP=PQ (1)
∴AF and EC bisect BD
In △APB
E is mid point of AB
EQ∥AP
By converse of MPT ( mid point theorem )
Q is mid point of PB
⇒PQ=QB (2)
By (1) and (2)
⇒PQ=QB=DP
AF and EC bisect BD..
Step-by-step explanation:
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