如图,△ABC是一个等边三角形,点D、E分别在AB、AC上,F是BE和CD的交点,已知∠BFC=120°.求证:AD=CE.
如图,△ABC是一个等边三角形,点D、E分别在AB、AC上,F是BE和CD的交点,已知∠BFC=120°.求证:AD=CE.
数学人气:730 ℃时间:2020-04-12 13:40:05
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证明:∵∠BFC=120°,∴∠ECF=∠BFC-∠CEB=120°-∠CEB,又△ABC是等边三角形,∴∠EBC=180°-60°-∠CEB=120°-∠CEB,∴∠ECF=∠EBC,即∠DCA=∠EBC,又∵△ABC是等边三角形,∴∠CAD=∠BCE=60°,AC=CB∴△ACD≌...
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