You cannot use ANY results from Euclidean geometry Only ones

You cannot use ANY results from Euclidean geometry. Only ones that are in neutral geometry.

There are three pairs of triangles that can be proved congruent in the following figure. Name the pairs and prove that they are congruent.

Triangles ABD and JGD can be proved conguent by AAA (three angles) criterion for congruence

<BAD = <DJG , being alternate interior angles formed by the two parallel lines AB and GJ cut by the transversal AJ.

By the same reason < BGJ = <ABD.

Also, <ADB = <GDJ , being vertically opposite angles.

Now, triangles AGJ and BJG can be proved conguent by SSS criterion (Three sides equal)

Obviously, from the figure, AG = BJ

AJ = BG

GJ = JG (common side)

Finally, the triangles ABG and BAJ can be proved conguent using SSS criterion

From figure, BG = AJ

AG = BJ

AB = BA (common side)

Hence the solution.