What does the locus of 2 intersecting lines form?

The correct answer identifies that the locus formed by two intersecting lines consists of the angle bisectors of the four angles that are created at the point of intersection. When two lines intersect, they form two pairs of vertical angles, each pair sharing a common angle. The angle bisectors of these angles are significant because they equally divide the angles into smaller angles, creating a relationship between the originating lines.

In a geometric context, this means that each pair of angle bisectors intersects at the point where the two original lines meet, leading to the formation of four distinct angle bisectors, each corresponding to the angles formed by the intersecting lines. This property is often utilized in various geometric proofs and theorems, demonstrating the symmetry and interrelationship of angles surrounding the intersection point.

The other choices do not capture the essence of what is formed by the intersection of two lines. For instance, while the extensions of the lines occur outside the intersection, they do not represent a specific locus related to the angles formed. Similarly, a triangle formed with the intersection point as the apex typically arises from connecting more than just the lines, while a quadrilateral would also involve additional points that are not representative of the simple intersection of the two lines. Therefore, the angle bisectors