Q. 74.6( 27 Votes )

In <span lang="EN

Answer :

Given:- AB||DE , AB=DE; BC||EF, BC=EF


Formula used:- SSS congruency rule


If all 3 sides of both triangle are equal then


Both triangles are congruent.


Solution:-


(1) In ABED


AB||DE


AB=DE


ABED is a parallelogram


If one pair of side in quadrilateral is equal and parallel


Then the quadrilateral is parallelogram.


(2) In BCFE


BC||EF


BC=EF


BCEF is a parallelogram


If one pair of side in quadrilateral is equal and parallel


Then the quadrilateral is parallelogram.


(3) As ABED is a parallelogram


BE||AD , BE=AD ;


As BCFE is a parallelogram


BE||CF , BE=CF ;


By concluding both above statements


AD||CF and AD=CF


ACFD is a parallelogram


If one pair of side in quadrilateral is equal and parallel


Then the quadrilateral is parallelogram


If ACDF is a parallelogram ;


Then


AC=DF [opposite sides of parallelogram are equal ]


(4) In Δ ABC and Δ DEF


AB=DE [Given]


BC=EF [Given]


AC=DF [Proved above]


Δ ABC Δ DEF [SSS congruency rule]


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