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Question

In a ABC,D and E are points on AB and AC respectively such that ADDB=AEEC and ADE=DEA. Prove that ABC is isosceles
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Solution

Since ADDB=AEEC, by converse of Thales theorem, DEBC
ADE=ABCand...(1) and
DEA=BCA....(2)
But, given that ADE=DEA...(3)
From (1),(2) and (3), we get ABC=BCA
AC=AB (If opposite angles are equal, then opposite sides are equal).
Thus, ABC is isosceles.

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