Mathematics
In the adjoining figure, AB = CD, CE = BF and ∠ACE = ∠DBF. Prove that
(i) △ACE ≅ △DBF
(ii) AE = DF.
Triangles
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Answer
(i) In △ACE and △DBF,
Given,
AB = CD
⇒ AB + BC = CD + BC
⇒ AC = BD.
∠ACE = ∠DBF (Given)
CE = BF (Given)
Hence, by SAS axiom △ACE ≅ △DBF.
(ii) We know that, △ACE ≅ △DBF.
We know that corresponding sides of congruent triangles are equal.
∴ AE = DF.
Hence, proved that AE = DF.
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