"direct" proof of Steiner-Lehmus Theorem - 珍珠湾ART

Got this proof from the internet. www.ddhw.com

As before, ABC is the triangle, BY, CZ the bisectors of B, C, with Y on AC, Z on AB. We have BY = CZ. Let E be the intersection of BY and CZ. Connect A, E.

Find the point D outside of edge AB so that BD = AZ and DY = AC. www.ddhw.com

So triangle DBY is congruent with AZC. Let the bisector of

A, D, B, Y are concyclic ( www.ddhw.com

Then A, D, F, E are concyclic (

Since AE = DF (DBY congruent with AZC) , we have AD // EF.

Therefore,