Final answer:
To prove that [NI) is the bisector of angle ONC, we need to show that the measure of angle NIA is equal to the measure of angle NIC. By using the properties of isosceles triangles and parallel lines, we can demonstrate that these angles are congruent.
Step-by-step explanation:
To prove that [NI) is the bisector of angle ONC, we need to show that the measure of angle NIA is equal to the measure of angle NIC. In triangle SON, since it is isosceles, we know that angles SNO and SON are congruent. Similarly, in triangle SON, angles NSO and NSO are congruent. Since the parallel line drawn at O to line SA intersects line SC at N, we can conclude that angle SNF is congruent to angle NIA. Similarly, since the parallel line drawn at N to line SO intersects line AC at I, we can conclude that angle NIC is congruent to angle FNC. Therefore, angle NIA and angle NIC are congruent, proving that [NI) is the bisector of angle ONC.