Test analysis: (1) Answer according to the judgment method of triangle congruence "SSS". (2) Prove the congruence of Rt△OMP and Rt△ONP with the judgment method "HL", and answer according to congruent triangles's equilateral. (3) Using the scale to make PM=PN, and then using "SSS" to prove the congruence of two triangles, we can get the solution:
△MOP and △NOP∴∠MOP=∠NOP.∴OP are bisectors of ∠AOB.
Problem analysis: (1) The triangular congruence method used by Teacher Li is "SSS".
(2) Xiao Cong's approach is correct. The reason for this is the following：
At ∴rt△omp≌rt△onp(hl). rt△OMP and Rt△ONP.
∴∠MOP=∠NOP.∴OP is the bisector of ∞∠AOB.
(3) As shown in the figure, ① Draw points M and N on OA and OB with scales on the scale, so that OM = ON② Make MP=NP with two scales, and cross at point P; ③ As a ray OP, OP is the bisector of ∠AOB.
Test site: 1. Congruent triangles's application; 2. Drawing (basic drawing).