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Question:

In given figure E is a point on side CB produced of an isosceles triangle ABC with AB=AC. If AD⊥BC and EF⊥AC, prove that △ABD≅△ECF.

Solution:

Given AB=AC
∴∠B=∠C.. (1)
In △ABD and △ECF
∠B=∠C (From 1)
∠ADB=∠EFC=90o [∵AD⊥BC and EF⊥AC,]
∴By AA Criterion of Similarity, △ABD≅△ECF [hence proved]