如图4-20.△ABC中,∠acb=90 bm=mc.cp⊥am于p如图4-20.△ABC中,∠ABC=90 BM=MC.CP⊥AM于P,交AB于D.求证角ABM=角BPM

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如图4-20.△ABC中,∠acb=90 bm=mc.cp⊥am于p如图4-20.△ABC中,∠ABC=90 BM=MC.CP⊥AM于P,交AB于D.求证角ABM=角BPM

如图4-20.△ABC中,∠acb=90 bm=mc.cp⊥am于p如图4-20.△ABC中,∠ABC=90 BM=MC.CP⊥AM于P,交AB于D.求证角ABM=角BPM
如图4-20.△ABC中,∠acb=90 bm=mc.cp⊥am于p
如图4-20.△ABC中,∠ABC=90 BM=MC.CP⊥AM于P,交AB于D.求证角ABM=角BPM

如图4-20.△ABC中,∠acb=90 bm=mc.cp⊥am于p如图4-20.△ABC中,∠ABC=90 BM=MC.CP⊥AM于P,交AB于D.求证角ABM=角BPM
∵CP⊥AM于P
∴CM^2=MP*MA
因为BM=CM
∴BM^2=MP*MA
∴BM/MA=MP/BM
∠PMB=∠AMB
∴△ABM∽△BPM
∴∠ABM=∠BPM