Question 1105835
CBD=BDH are alternate interior angles.  They are equal if the lines are parallel.
CBD=ABJ because of vertical angles.
Further, ABJ=BDH, and those are corresponding angles that are equal.
That should be enough
BDH=JHI because angle IHG is supplementary to ABJ
JHI is supplementary to IHG.
That makes it equal to ABJ, which is supplementary, and also to BDH.
When JHI is equal to BDH, corresponding angles are equal, and the lines are parallel.