Answer:
False
Explanation:
P is not necessarily on the angle bisector of angle A.
Attached is an example of a carefully constructed shape (so that it's easy to see the measurements):
- Angle A measures 45° (again, for convenience)
- Point P is 4 units to the right of and 3 units above point A.
- Point P forms a right angle with two congruent line segments, each of which terminate on the rays extending from Point A, forming angle A.
- The lower point is 8 units to the right of point A; the upper point is 7 units to the right of and 7 units above point A.
- The length of the two line segments is 5 units, and thus they are congruent.
Visually, point P is not on the angle bisector of angle A.
While having two adjacent congruent segments is necessary for P to be on the bisector of angle A, it is not sufficient. The segments on the rays from A to the end of those segments would also need to be a pair of congruent adjacent sides (forming a kite). For a kite, the diagonal from the point between one pair of adjacent congruent sides to the point between the other pair of adjacent congruent sides does form an angle bisector with both angles.