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Similar triangles

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For triangle ABC ( order in anti-clockwise direction), D is a point on AB and E is a point on AC such that CD perpendicular to AB and BE perpendicular to AC. Prove that angle EDC = angle EBC by proving of similar triangles ( theorems of circle is not allowed).

最佳解答:

Let DC and DE meet at point F, then△BFD ~△CFE, so in BF/DF = CF/EF,and ㄥBFC = ㄥDFE so△BFC~△DFE (SAS) so angle EDC = angle EBC

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