如图1,若OC是∠AOB的平分线,点P在OC上,PD⊥OA,PE⊥OB,垂足分别是D、E,则PD=PE;反之,若PD⊥OA于D,PE⊥OB于E,且PD=PE,则点P在∠AOB的平分线上,即OC平分∠AOB.这就是角平分线的性质定理及其逆定理,图1是定理的基本图形,很多几何题都含有该图的“影子”,因而可以简捷地利用基本图 As shown in Figure 1, if OC is the bisector of AOB, point P is on OC, PD⊥OA, PE⊥OB, and if the feet are D, E, then PD=PE; conversely, if PD⊥OA is at D, PE ⊥OB in E, and PD=PE, point P is on the bifurcation line of ∠AOB, ie OC bisection ∠AOB. This is the property theorem of the bisector and its inverse theorem. Figure 1 is the basic graph of the theorem, many geometries The questions contain the “shadow” of the map, so that the basic map can be used simply and easily.