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角平分线的性质告诉我们,角的平分线上的点到角的两边的距离相等.它的基本图形如图1.已知:OC平分∠AOB.P为OC上一点,且PD⊥OA于D点,PE⊥OB于E点.结论:PD=PE.这是角平分线的基本性质.它在解题中十分有用,千万不可小视它.一、证明线段相等(一)过角平分线上一点作角的一边的垂线段例1如图2,AD⊥DC于D点,BC⊥CD于C点.∠BAD的平分线AE和∠ABC的平分线BE交于点E,且点E在CD上.求证:DE=CE.
The nature of the angle bisector tells us that the angles on the bisector of the angle are equally equal to the two sides of the angle. Its basic shape is shown in Fig. 1. Known: OC bisection ∠AOB.P is one point on OC, and PD⊥OA is Point D, PE⊥OB at point E. Conclusion: PD=PE. This is the basic nature of the angle bisector. It is very useful in problem solving and must not be underestimated. First, prove that the line segments are equal (a) the angular division A vertical line on one side of the corner is shown in Fig. 2, where AD ⊥ DC is at D, BC ⊥ CD is at C. The bisector AE of ∠BAD and the bisector BE of ∠ ABC are intersected at point E, and E on the CD. Proof: DE=CE.