In △ ABC, ad bisects ∠ BAC, intersects BC with D, EF ‖ ad, intersects AC with E, intersects the extension of BA with F. it is proved that △ AEF is an isosceles triangle

In △ ABC, ad bisects ∠ BAC, intersects BC with D, EF ‖ ad, intersects AC with E, intersects the extension of BA with F. it is proved that △ AEF is an isosceles triangle

It is proved that: ∵ EF ‖ ad, ∵ f = ∵ bad, ∵ AEF = ∵ DAC. ∵ ad bisects ∵ BAC, ∵ bad = ∵ DAC, ∵ f = ∵ AEF, ∵ AE = AF, i.e. △ AEF is isosceles triangle