For 9:
1. Angle T and angle M are congruent because they are given
2. The line AH bisects angle THM because it is given
3. Angle 1 and angle 2 are congruent because of properties of angle bisection
4. The line AH is congruent to the line HA because of the reflexive property
5. Triangle TAH is congruent to triangle MHA because of AAS
6. The line TA is congruent to MA because of congruent triangles
For 10:
1. Angle H and angle J are congruent because it is given
2. G is the midpoint of FI because it is given
3. Angle 1 and angle 2 are congruent because they are vertical angles
4. Line HG is equal to line JG because of properties of midpoints
5. The triangles HIG and JFG are congruent because of AAS
6. The lines HI and JF are congruent because of congruent triangles
