1.

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Answer»

Given :


1. AB = CD

2. CE = BF

3. ∠ ACE = ∠ DBF


To prove :


1. Δ ACE ≡ Δ DBF

2. AE = DF


Proof :


AB = CD


Adding BC on both sides to the above equation we GET,


AB + BC = CD + BC

=> AC = BD ----( Equation 1 )


Consider Δ ACE and Δ DBF


AC = BD ( S ) ( From Equation 1 )

∠ACE = ∠ DBF ( A ) ( Given )

CE = BF ( S ) ( Given )


Therefore by SAS criteria, we can say that,


Δ ACE ≡ Δ DBF


By CPCT, ( Corresponding parts of congruent TRIANGLES ) we can say that,


AE = DF


Hence PROVED



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