∠ FHG= ∠ HKJ ------Given
FH = HK Because H is midpoint of FK
FG ∥HJ Given thus
∠ HFG = ∠ KHJ Corresponding angles
Hence the triangle FHG is congruent to HKJ by ASA criterion
I have a proof here with me and I just want to see if I am correct.
So we're trying to prove these triangles are congruent and then apply the CPCTC method to prove Segment FG is congruent to segment HJ.
This is what I have so far: (I mentioned HG is congruent to HG and KJ is congruent to KJ by Identity, but I'm not sure if I can conclude these triangles are congruent after that)
Proof and Reasons:
1) Angle 1 is congruent to Angle 2 ------- 1) Given
2) Line segment FH is congruent to Line segment HK --------- 2) The Midpoint of a line segment forms 2 congruent segments
3) Line segment HG is congruent to HG, line segment KJ is congruent to KJ ----------- 3) Identity
4) Triangle FHG is Congruent to Triangle HKJ ----------- 4) SAS
5) Line segment FG is congruent to Line segment HJ ------- 5) CPCTC