Answer:

The second question:

Answer:

The third question:

Answer:

This part of the extended data mainly examines the knowledge points of the angular bisector:

Draw a ray from the vertex of an angle (the line is inside the angle) and divide the angle into two identical angles. This ray is the bisector of the angle. The bisector of an angle is the locus of points in the shape of an angle that are equidistant from both sides of the angle. The two angles divided by the bisector are equal, both equal to half the angle. (Definition) The distance between points on the bisector of an angle is equal to both sides of the angle.

The bisector of an angle of a triangle intersects the opposite side of the angle, and the line segment connecting the vertex of the angle and the opposite side is called the bisector of the triangle (the bisector of the inner angle of the triangle). By definition, the bisector of a triangle is a line segment. Because a triangle has three internal angles, it has three bisectors. The intersection of the bisectors of a triangle must be inside the triangle.

Judge:

The points from the inside of the angle to both sides of the angle are on the bisector of this angle.

So according to the axiom of straight line.

It is proved that PD⊥OA is known in D, PE⊥OB is known in E, and PD=PE. Prove that OC divides ∠AOB equally.

Proof: In Rt△OPD and Rt△OPE:

OP=OP，PD=PE

∴Rt△OPD≌Rt△OPE(HL)

∴∠ 1=∠2

∴ OC equal division ∠AOB