AD是三角形ABC的角平分线,AD的中垂线交AB于F,交BC的延长线于E,连结DF,求证∠EAC=∠B.
人气:292 ℃ 时间:2019-08-19 21:09:23
解答
证明:三角形ADE为等边三角形,所以∠ADE=∠EAD,∠ADE=∠B+∠BAD,∠EAD=∠DAC+∠EAC,因为AD是三角形ABC的角平分线,所以∠BAD=∠DAC,于是∠EAC=∠B.
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