等腰三角形ABC中,角A=36度,角B=72度,角C=72度,请同学们想一想,如何添一条线,将等腰三
\u5728\u25b3ABC\u4e2d,\u2220A=36\u00b0,\u2220C=72\u00b0,\u8bf7\u4f60\u505a\u4e00\u6761\u7ebf,\u4f7f\u5f97\u56fe\u4e2d\u51fa\u73b0\u4e09\u4e2a\u7b49\u8170\u4e09\u89d2\u5f62,\u5e76\u8bf4\u660e\u7406\u7531\u3002\u8fd9\u662f\u9ec4\u91d1\u4e09\u89d2\u5f62\u4e2d\u7684\u4e00\u79cd(\u53e6\u4e00\u4e2a\u9876\u89d2\u4e3a108\u00b0\u7684\u7b49\u8170\u4e09\u89d2\u5f62)\uff0c
\u53ea\u8981\u8fc7\u5e95\u8fb9\u4e0a\u4efb\u4e00\u7aef\u70b9\uff0c\u4f5c\u5185\u89d2\u7684\u5e73\u5206\u7ebf\uff0c\u4ea4\u5bf9\u8fb9\u4e8e\u4e00\u70b9\uff0c
\u5219\u5206\u6210\u7684\u4e24\u4e2a\u4e09\u89d2\u5f62\u4e5f\u90fd\u662f\u9ec4\u91d1\u4e09\u89d2\u5f62(\u5373\u8fd8\u53ef\u4ee5\u7ee7\u7eed\u5206\u4e0b\u53bb)\u3002
\u89e3\uff1a\u7531\u5224\u522b\u5f0f \u25b3=m^2-4\u00d7(2-1/2m)
=m^2+2m-8
=(m+4)(m-2)
\uff081\uff09\u82e5\u65b9\u7a0b\u6709\u4e24\u7b49\u6839\uff0c\u5219m=-4\u62162\uff0c\u6b64\u65f6b=c
\u5f53m=2\u65f6\uff0c \u89e3\u5f97 x=-1\uff08\u820d\uff09
\u5f53m=-4\u65f6\uff0c\u4ee3\u5165\u65b9\u7a0b\u89e3\u5f97 x=2, \u5373\u6b64\u65f6b=c=2
\u6240\u4ee5\u5468\u957f\u4e3aa+b+c=3+2+2=7
\uff082\uff09\u82e5\u65b9\u7a0b\u6709\u4e24\u4e0d\u7b49\u6839\uff0c\u5219\u5bf9\u7b49\u8170\u4e09\u89d2\u5f62\u800c\u8a00\uff0cb\u6216c\u7b49\u4e8e3\uff0c\u5373\u65b9\u7a0b\u6709\u4e00x=3\u6839\uff0c
\u5c06x=3\u5e26\u5165\u539f\u65b9\u7a0b\uff0c \u5f97 3^2+3m+2-1/2m=0
\u89e3\u5f97 m=-22/5
\u5c06m=-22/5\u5e26\u5165\u65b9\u7a0b\uff0c\u6709 x^2-22/5x+2-1/2\u00d7(-22/5)=0
\u5316\u7b80\u5f97 x^2-22/5x+21/5=0
(5x-7)(x-3)=0
x=3\u62167/5\uff0c \u6b64\u65f6\u6ee1\u8db3\u4e09\u89d2\u5f62\u4e09\u8fb9\u5173\u7cfb
\u6240\u5f97\u4e09\u89d2\u5f62\u5468\u957f\u4e3a3+3+7/5=37/5
\u7efc\u5408\u5f97 \u4e09\u89d2\u5f62ABC\u7684\u5468\u957f\u4e3a7\u621637/5
\u6ee1\u610f\uff0c\u8bf7\u53ca\u65f6\u91c7\u7eb3\uff01
在取等腰三角形一腰的中点，并与其对顶点相连，就又得到2个等腰三角形，也就是说，我们只要取三个角为36、72、72度的等腰三角形的其中一腰的中点，并与其对顶点相连，就可以将一个等腰三角形分成两个等腰三角形，并且可以一直继续进行下去。
绛旓細鈭A=36搴︺傚洜涓烘槸绛夎叞涓夎褰鎵浠モ垹B=鈭燙=72搴 BD鏄骞冲垎绾 鎵浠モ垹ABD=鈭燚BC 鍚岀悊鈭燗CE=鈭燛CB=36搴︽墍浠ュ緱鍑築E=BC 鍥犱负 鈭燘EC=108搴︽墍浠モ垹CED=72搴 鎵浠E=CD 鍚岀悊BD锛滲C鎵浠E+DE=DB鐒跺悗甯﹀叆k 灏卞ソ浜
绛旓細D. 璇曢鍒嗘瀽锛氱敱宸茬煡鏉′欢锛屾牴鎹绛夎叞涓夎褰鐨勫畾涔夊強绛夎瀵圭瓑杈瑰厛寰楀嚭鈭燗BC鐨勫害鏁帮紝鐢扁垹ABC鐨勫钩鍒嗙嚎浜C浜嶥锛屽緱鍒板叾瀹冭鐨勫害鏁帮紝鐒跺悗杩涜鍒ゆ柇锛氣埖鍦ㄢ柍ABC涓紝鈭A=36掳锛屸垹C=72掳锛屸埓 .鈭碅B=AC锛屸埓鈻矨BC鏄瓑鑵颁笁瑙掑舰.鈭礏D骞冲垎鈭燗BC浜C浜嶥锛屸埓鈭燗BD=鈭燚BC=36掳.鈭碘垹A=鈭燗BD=36掳锛屸埓鈻...
绛旓細浣滃簳杈笲C涓嚎AE浜C浜嶦,鍥犱负绛夎叞涓夎褰搴曡竟涓嚎銆侀珮鍜岄《瑙掑钩鍒嗙嚎閲嶅悎锛屾墍浠ュ彲寰楋細BE=CE AE鈯C 鈭燘AE=鈭燙AE 鈭礎B=AC 鈭燘AC=36掳 鈭粹垹ABC=鈭燙=72掳 鈭燘AE=鈭燙AE-18掳 鈭礏D骞冲垎鈭燗BC 鈭粹垹ABD=鈭燙BD=36掳 鍚岀悊鍙畻鍑衡垹BDC=72掳 鈭碘垹BAC=鈭燗BD=36掳 鈭燘DC=鈭燙=72掳 ...
绛旓細AD=10*0.618=6.18 cm鍒嗘瀽锛氬叧閿槸鐪婥D 鍜孉D鐨勫ぇ灏忛棶棰,灏辩煡閬撹皝鏄粍閲戝垎鍓茬殑澶х殑涓杈逛簡.鍥犱负AB=AC ,鈭A=36搴︽墍浠モ垹ABC=鈭燘CD=72搴︽墍浠モ垹ABD=鈭燙BD=36搴︽墍浠 AD=BD 鍥犱负鈭燙BD < 鈭燘CD,鐢卞ぇ瑙掑澶ц竟鎵浠D
绛旓細鍥犱负涓夎褰BC涓绛夎叞涓夎褰,涓瑙扐=36搴,AB=AC,鎵浠ヨB=瑙扖=72搴︿綔瑙払鐨勫钩鍒嗙嚎BD浜C浜嶥,鏈夎CBD=36搴,瑙BDC=72搴︽墍浠ヤ笁瑙掑舰ABC鐩镐技浜庝笁瑙掑舰BCD,浠庤孉B/BC=BC/CDBD=BC=AD鎵浠D=AC-AD=AB-BC鍗矨B/BC=BC/(AB-BC)AB^2-AB...
绛旓細锛2锛夆埖鈭A=36 掳锛 鈭粹垹ABC=鈭燙=锛180 掳-36 掳锛壝2=72 掳锛 鈭礏D骞冲垎鈭ABC锛 鈭粹垹ABD=鈭燚BC=72掳 梅2=36 掳锛 鈭粹垹CDB=180 掳-36 掳-72 銆 =72掳锛 鈭碘垹A=鈭燗BD=36掳锛屸垹C=鈭燙DB=72掳锛 鈭碅D=DB锛孊D=BC锛 鈭粹柍ABD鍜屸柍BDC閮芥槸绛夎叞涓夎褰锛
绛旓細鈭粹垹BGD=鈭A=36掳鏍规嵁寮﹀垏瑙掑畾鐞,鈭燘DH=鈭燘GD=36掳,鈭粹垹BHD=180掳-鈭ABC-鈭燘DH=180掳-72掳-36掳=72掳鈭碆D=HD鍚岀悊鍙瘉,DE=DC鈭礑G=DF鈭粹垹DGF=鈭燚FG=72掳鈭粹垹GDF=36掳鈭礕F鈭=BC鈭村洓杈瑰舰GFCD涓哄钩琛屽洓杈瑰舰鈭粹垹GDC=鈭燝FC=108掳鈭粹垹EDF=鈭燝DC-鈭燝DF-鈭燙DE=108掳-36掳-36掳=36掳=鈭燚FE鈭碊E=EF...
绛旓細绛夎叞涓夎褰BC涓,椤剁偣CA=36搴︼紝鈭燗BC=(180-36)=72 BD涓瑙扐BC,鈭燗BD=72/2=36掳 鈭A=鈭燗BD,鍒橞D=AD,,鈭燘DC=鈭燗+鈭燗BD=72=鈭燗CB 锛屸柍BDC涓虹瓑鑵扳柍锛孊D=BC=AD锛 AB=AC BC/AB=DC/AD瑙掑钩鍒嗙嚎瀹氱悊 鍒橝D/AC=BC/AB=DC/AD=DC/BC=sin36掳/sin72掳=1/2cos36掳 ...
绛旓細鍦绛夎叞涓夎褰BC涓,椤惰瑙扐=36搴,BD涓鸿ABC鐨勫钩鍒嗙嚎 瑙扐BC=瑙扖=72掳 瑙扐BD=瑙扖BD=36掳=瑙扐 鎵浠D=BD 瑙払DC=瑙扐+瑙扐BD=36掳+36掳=72掳=瑙扖 鎵浠C=BD 鎵浠D=BC 涓夎褰CD鐩镐技涓夎褰BC AC/BC=BC/CD AD^2=BC^2=AC*CD=AC*(AC-AD)(AC/AD)^2-AC/AD-1=0 AC/AD=(1+5^...
绛旓細鈭碘垹A=36掳锛孉B=AC锛屸埓鈭燗BC=鈭燙=72掳锛屸埖BD骞冲垎鈭ABC锛鈭粹垹ABD=鈭燙BD=36掳=鈭燗锛屸埓AD=BD 鈭碘垹BDC=鈭燗+鈭燗BD=72掳=鈭燙锛屸埓BD=CB 鈭碆C=AD锛屸埖鈭燙=鈭燙锛屸垹A=鈭燘CD锛屸埓鈻矨BC鈭解柍BDC锛屸埓CD/CB=CB/CA 鈭碈D*CA=BC²=AD²锛屽嵆D鏄疉C鐨勯粍閲戝垎鍓茬偣锛屸埓AD/AC=(鏍瑰彿5-1...
