I expect you wish to prove the triangles AGD and AHK are similar and

also that triangles AGF and AHI are also similar in the attached figure.

As lines HK and GD are parallel (by construction), angles HKA and GDA are

congruent. Also angle DAG is common to both triangles all of the angles in

AGD are congruent to the corresponding angles in AHK, and so these

triangles are similar.

Now look at angles HIA and GFA, these are both right angles (by

construction), and angle HAI is common to both triangles AGF and AHI

so these two triangles have two equal angles, hence all the corresponding

angles are congruent, and so the triangles are similar.

RonL