如图,△ABC中,点D、E分别在边AB、AC上,BE、CD相交于点F,且AD?AB=AE?AC.求证:(1)△ABE∽△ACD;(

2025-01-06 16:52:01
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回答1:

解答:证明:(1)∵AD?AB=AE?AC,
∴AD:AE=AC:AB,
∵∠A=∠A,
∴△ABE∽△ACD;

(2)∵△ABE∽△ACD,
∴∠ABE=∠ACD,
∵∠BFD=∠CFE,
∴△BFD∽△CFE,
∴FD:FE=FB:FC,
∴FD?FC=FB?FE.