Final answer:
To prove that EF and HF are congruent, we need to show that triangles EFG and HFG are congruent using the SAS criterion.
Step-by-step explanation:
In order to prove that EF and HF are congruent, we need to provide evidence that they have the same length. This can be done by showing that they are corresponding sides of congruent triangles. If we can establish that triangles EFG and HFG are congruent, then we can conclude that EF and HF are congruent.
One way to prove the congruence of triangles is by using the Side-Angle-Side (SAS) congruence criterion. This means that if we can show that the corresponding sides of two triangles are congruent and that the included angles between those sides are also congruent, then we can conclude that the triangles are congruent.
So, to prove that EF and HF are congruent, we need to show that triangle EFG and triangle HFG satisfy the SAS criterion. We can do this by demonstrating that side EF is congruent to side HF and that angle EFG is congruent to angle HFG. Once we establish the congruence of the triangles, we can conclude that EF and HF are congruent.