In figure E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If `A D_|_B C`and`E F_|_A C`, prove that`DeltaA B D ~DeltaE C F`.

Explanation

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.


This is referred to as AA similarity criterion for two triangles.


In `ΔABD` and `ΔECF`


`∠ADB = ∠EFC = 90º` [`∵ AD ⊥ BC` and `EF ⊥ AC`]
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