Mathematics
In the given figure, AD = AE and AD2 = BD x EC. Prove that: triangles ABD and CAE are similar.
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Answer
From figure,
⇒ ∠ADE = ∠AED [Angles opposite to equal sides of a triangle are equal].
⇒ 180° - ∠ADE = 180° - ∠AED
⇒ ∠ADB = ∠AEC
Given,
⇒ AD2 = BD x EC
⇒ AD x AD = BD x EC
⇒ AD x AE = BD x EC
⇒
∴ △ABD ~ △CAE [By SAS]
Hence, proved that △ABD ~ △CAE.
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