AB/BD=BC/BE=CA/ED,求证:∠ABD=∠CBE,∠BAD=∠BCE

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AB/BD=BC/BE=CA/ED,求证:∠ABD=∠CBE,∠BAD=∠BCE
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AB/BD=BC/BE=CA/ED,求证:∠ABD=∠CBE,∠BAD=∠BCE
AB/BD=BC/BE=CA/ED,求证:∠ABD=∠CBE,∠BAD=∠BCE

AB/BD=BC/BE=CA/ED,求证:∠ABD=∠CBE,∠BAD=∠BCE
证明:
∵AB/BD=BC/BE=CA/ED
∴△ABC∽△DBE
∴∠ABC=∠DBE
∴∠ABC-∠CBD=∠DBE-∠CBD
∴∠ABD=∠EBC
∵∠ABD=∠EBC,AB/BD=BC/BE
∴△ABD∽△CBE
∴∠BAD=∠BCE