SOLUTION: I can't figure out the correct reason in this proof for #4. Can you help me? Here it is: 1. line segment GF is perpendicular to AC given 2. angles AGF and CGF

Question 41874: I can't figure out the correct reason in this proof for #4. Can you help me? Here it is:
1. line segment GF is perpendicular to AC given
2. angles AGF and CGF are congruent given
3. line segments GF and GF are congruent reflexive property
4. triangles GFA and GFC are congruent (? HELP)
5. line segments AG and CG CPCTC
6. triangle AGC is isosceles a triangle is an
isosceles triangle if
1 of its vertices is
contained by a
perpendicular bisector
Answer by PaulAllen65270(19) (Show Source): You can put this solution on YOUR website!
Two triangles are congruent if a line angle line are congruent. or angle line angle are congruent. So you need two lines and an angle that connects them to be congruent for the triangle to be congruent. When a line is perpendicular then each of the bisected parts are going to be congruent, there is one leg of the triangle. GF is going to be congruent because it is the same line for both triangles. The angle is going to be congruent becuase it is formed from the perpendicular lines. Hopefully this made this as clear as mud (haha).
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