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Question 934336: Image and video hosting by TinyPic
Answer by mananth(16946) About Me  (Show Source):
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angle CDE = Angle CED ( Given)
Therefore CD congruent - CE ( converse of Isosceles angle theorem)
But CD = BE given
Therefore CE = BE
Therefore angle ECB = angle EBC ( isosceles angle theorem)........(1)
In triangle CED angle CEB = angle ECD + angle EBC ( exterior angle theorem)
Therefore angle CEB = 2 angle EBC ( angle ECB = angle EBC ) from (1)
angle DCA + angle DAC = angle CDE ( exterior angle theorem)
But angle CDE =angle CED ( Isosceles Triangle)
angle DCA + angle DAC=angle ECD + angle EBC = 2angle B
Therefore angle CED = angle DCA + angle DAC =2 angle B
Therefore angle A = angle B
Therefore AC = BC ( converse of isosceles angle theorem