I need help making a proof table with statements and reasons.
View attachment 4398
Let's see if we can think through a PLAN for this proof.
You're asked to prove that triangle EFI is isosceles. What would it take for us to be able to say that triangle is isosceles? By definition, a triangle is isosceles if it has at least two equal sides. So, before we can call triangle EFI an isosceles triangle, we need to find that at least two of its sides are congruent. Maybe we could show that sides EI and FI are congruent. I see that EI is a side of triangle EHI, and FI is side of triangle FGI. If those two triangles turn out to be congruent, then we could use the fact that corresponding parts of congruent figures are congruent to conclude that EI and FI are congruent, which would, in turn, allow us to say that triangle EFI is isosceles.
Look at the given information to see what it tells you about the parts of triangles EFI and FGI......do you have enough information to say those triangles are congruent?
So....here's the plan. Use the given information (and what you know because of what is given) to show that triangles EFI and FGI are congruent. Then, use the fact that corresponding parts of congruent figures are congruent to say that EI and FI are congruent. And once you have done that, you can say that triangle EFI is isosceles because of the definition of an isosceles triangle.
Perhaps this will help you to write down the statements and reasons that will complete the proof.