Question

in the adjoining figure,DC||AB,AD=BC.Prove using the concept of congruent triangles that AE=BF.

Answer 1

IN THE ADJACENT FIGURE
DECF IS ARECTANGLE SO DE=CF⇒1
AS,DC||Ab,AB IS A TRANSVERSALSO ANGLE AED=ANGLEBFC⇒2GIVEN AD=BC⇒3
FROM1,2,3
BY RHS congruency
triangleAED=TRIangleDFC
BY CPCT
AE = BF

Answer 2

IN THE ADJACENT FIGURE
DECF IS A RECTANGLE SO DE = C ---(i)
AS,DC||AB
AB IS A TRANSVERSE
 ALSO ∠AED = ∠BFC ---(ii)
GIVEN AD=BC ---(iii)
FROM (i), (ii) and (iii)
BY RHS congruency
ΔAED = ΔDFC
BY CPCT
AE = BF