Question

Anyone know how to work this out?

Answer 1

Well you know that all sides of a rhombus are equal menaing GD AND FE HAVE THE SAME LENGTH

And you know that two sets of angles are equal because the rhombus is a parallelogram meaning angles GDH is equal to angle HFE and vise versa with angles HGD And angle FEH ( z- pattern) - same angles also mean they are the same in length

Lastly angles DHG and angles FGE are the same because the are opposite angles

Therefore the two triangles a re congruent

Answer 2

The first and crucial thing we want to take notice is that the lines DF and EG intersect at point H which creates 4 different triangles in the rhombus. The innermost angles of DGH and EFH are vertical angles and vertical angles are congruent. So if the angles of the triangles are congruent than the triangles themselves are congruent. This is supported by the vertical angles theorem.