congruence of triangles: In triangles ABC and DEG we are given that AB=DE and AC=DG

[egyrak]

In triangles ABC and DEG we are given that AB=DE and AC=DG . AX is the angle bisector of BAC meeting BC in X and DY is the angle bisector of EDG meeting EG in Y. If AX=DY then prove that the triangles ABC and DEG are congrunt

 

[Deleted member 4993]

In triangles ABC and DEG we are given that AB=DE and AC=DG . AX is the angle bisector of BAC meeting BC in X and DY is the angle bisector of EDG meeting EG in Y. If AX=DY then prove that the triangles ABC and DEG are congrunt

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[egyrak]

I am sorry but I am stuck in this problem . I tried to assume that the two triangles are not congrunt and I can not complete . If any one can help.

 

[Deleted member 4993]

In triangles ABC and DEG we are given that AB=DE and AC=DG . AX is the angle bisector of BAC meeting BC in X and DY is the angle bisector of EDG meeting EG in Y. If AX=DY then prove that the triangles ABC and DEG are congrunt

First draw the triangles.

Assume that mBAC = 2Θ and mEDG = 2Φ. You need to prove Θ = Φ

Since AX and DY are bisectors, we know that

BX/XC = AB/AC = DE/DG = EY/YG.

Now continue....

 

[egyrak]

Thank you . Now BX= k EY and XC= k YG but now I am still confused . Shall I try to prove that k=1 or try to prove that the angles equal ?

 

[egyrak]

Please if I can get more help in this problem because I am still stuck ! with thanks for all