Q. 65.0( 2 Votes )

ΔABC and ΔDEF are two triangles such that AB, BC are respectively equal and parallel to DE, EF; show that AC is equal and parallel to DF.

Answer :

In the ΔABC and ΔDEF,
AB = DE and AB ïï DE
BC = EF and BC ïï EF
To Prove:   AC = DF and AC ïï DF
Construction: Join AD, CF and BE
Proof: Since AB = DE and AB ïï DE
... Quadrilateral ABED is a parallelogram (one pair of opposite sides are equal and parallel)
... AD = BE and AD ïï BE .....(i)
Similarly quadrilateral BEFC is a parallelogram
... BE = CF and BE ïï CF......(ii)
From (i) and (ii) we get,  
AD = CF and AD ïï CF
... ADFC is a parallelogram
... AC = DF and AC ïï DF

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