如图,Rt△ABC中,∠ACB=90°,AC=BC,点D是AB的中点,BE平分∠ABC,分别交A...
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发布时间：2024-10-24 18:24
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时间：2024-11-21 23:15
如图，过点E作EH⊥AB于H，
∵BE平分∠ABC，
∴EH=EC，
∵∠ACB=90°，AC=BC，EG∥AB，
∴△ABC、△AEH和△ECG都是等腰直角三角形，
∴AE=2EH，EG=2EC，
∴EG=AE，故①正确；
由等腰直角三角形的性质可得，BG=EG=2CG，BD=22（CG+2CG）=（22+1）CG，
∴BG≠BD，
∴∠BGD≠∠BDG，故②错误；
又∵AE=2EH=2CE，
∴S△ABE=2S△CBE，故③错误；
∵BE平分∠ABC，
∴∠ABE=∠CBE=22.5°，
∵点D是AB的中点，
∴CD⊥AB，
∴∠BDF=∠ACB=90°，
∴△BDF∽△BCE，
∴DFCE=BDBC=22，
又∵∠BEG=∠CGE-∠CBE=45°-22.5°=22.5°，
∴∠CBE=∠BEG，
∴BG=EG，
又∵EG=2CE，
∴DF=22CE=22×22BG=12BG，故④正确；
由等腰直角三角形的性质可得，BC=2CD，
CF=CD-DF=22BC-12BG，
∵CG=22EG=22BG，
∴BC=已赞过已踩过你对这个回答的评价是？评论收起 // 高质or满意or特型or推荐答案打点时间 window.iPerformance && window.iPerformance.mark('c_best', +new Date); 推荐律师服务：若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询 ._1uevpeq{zoom:1;background-color:#fff;border:0;margin-bottom:10px;padding:30px 0 20px 42px;position:relative}._1uevpeq.ec-1841{padding:20px 0}._1uevpeq.ec-2246{padding:20px 0 10px}.ec-1841 .y7we4hu{font-size:16px;margin-bottom:-5px}.y7we4hu{color:#7a8f9a;height:25px;line-height:25px;overflow:hidden;position:relative}.y7we4hu h2{margin:0;padding:0}.y7we4hu:after{clear:both;content:" ";display:block;height:0;visibility:hidden}a.tycfu7u{color:#666;float:right;font-size:12px;margin-left:8px;text-decoration:none}.hhhv6ex{color:#666;font-size:13px;line-height:normal;line-height:20px;margin-top:10px}.vnsdjzp{margin-top:15px;position:relative}.vnsdjzp h3{font-weight:400;padding:0}.vnsdjzp a{text-decoration:none}.vnsdjzp em{color:#d81419;font-style:normal}.ec-2246 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