11[1].3.1角平分线的性质(1min.ppt

Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 1、怎样用尺规作角的平分线. 角的平分线上的点到角的两边的距离相等 2、角的平分线的性质: OCB 1 A2 P DE PD ⊥ OA , PE ⊥ OB ∵∵ OC 是∠ AOB 的平分线∴ PD = PE 用数学语言表述: Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. ?反过来,到一个角的两边的距离相等的点是否一定在这个角的平分线上呢? 已知:如图,QD ⊥OA,QE⊥OB, 点D、E为垂足, QD=QE. 求证:点 Q在∠AOB 的平分线上. Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 证明: ∵∵ QD ⊥ OA , QE ⊥ OB (已知), ∴∠ QDO =∠ QEO = 90 °(垂直的定义) 在 Rt △ QDO 和 Rt △ QEO 中 QO = QO (公共边) QD=QE ∴ Rt △ QDO ≌ Rt △ QEO ( HL ) ∴∠ QOD =∠ QOE ∴点Q在∠AOB 的平分线上已知:如图,QD ⊥OA,QE⊥OB, 点D、E为垂足, QD=QE. 求证:点 Q在∠AOB 的平分线上. Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 角平分线的性质 2:到角的两边的距离相等的点在角的平分线上。∵∵QD⊥OA,QE⊥OB,QD=QE. ∴点Q在∠AOB 的平分线上. 用数学语言表示为: 角的平分线上的点到角的两边的距离相等. ∵∵QD⊥OA,QE ⊥OB, 点Q在∠AOB 的平分线上∴QD=QE Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 例题:如图, △ABC 的角平分线 相交于点 P, 求证:点 P到三边 AB、BC、CA的距离相等∵BM是△ABC 的角平分线,点P 在BM上, ABC P M N DE F ∴PD=PE (角平分线上的点到这个角的两边距离相等). 同理,PE=PF. ∴PD=PE=PF. 即点P到三边 AB、BC、CA的距离相等证明:过点 P作 PD ⊥ AB 于D, PE ⊥ BC 于E, PF ⊥ AC 于F Evaluation only. Evaluation only. Created with