Question
In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see Fig.). Show that AD = AE
✓
Answer
In $\triangle$ ABD and $\triangle$ACE,
AB = AC (Given) ...(1)
$\angle$ B = $\angle$C (Angles opposite to equal sides) ...(2)
Also, BE = CD
So, BE – DE = CD – DE
That is, BD = CE ...(3)
So, $\triangle$ ABD $\cong$ $\triangle$ ACE (Using (1), (2), (3) and SAS rule).
This gives AD = AE (CPCT)
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