(2016湖南省邵阳市)尤秀同学遇到了这样一个问题:如图1所示,已知AF,BE是△ABC的中线,且AF⊥BE,垂足为P,设BC=a,AC=b,AB=c.
求证:
.
该同学仔细分析后,得到如下解题思路:
先连接EF,利用EF为△ABC的中位线得到△EPF∽△BPA,故
,设PF=m,PE=n,用m,n把PA,PB分别表示出来,再在Rt△APE,Rt△BPF中利用勾股定理计算,消去m,n即可得证.
(1)请你根据以上解题思路帮尤秀同学写出证明过程.
(2)利用题中的结论,解答下列问题:
在边长为3的菱形ABCD中,O为对角线AC,BD的交点,E,F分别为线段AO,DO的中点,连接BE,CF并延长交于点M,BM,CM分别交AD于点G,H,如图2所示,求
的值.
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6e2948f17dc94a1af0648c14d01809.png)
该同学仔细分析后,得到如下解题思路:
先连接EF,利用EF为△ABC的中位线得到△EPF∽△BPA,故
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe87c62addb497dce9c3b81e0db924a.png)
(1)请你根据以上解题思路帮尤秀同学写出证明过程.
(2)利用题中的结论,解答下列问题:
在边长为3的菱形ABCD中,O为对角线AC,BD的交点,E,F分别为线段AO,DO的中点,连接BE,CF并延长交于点M,BM,CM分别交AD于点G,H,如图2所示,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1e478ff979f8557e0f169eaf22f154.png)
![](https://img.xkw.com/dksih/QBM/2018/2/6/1876482912264192/1883842650914816/STEM/d647f2ecd9dc427c9db49cf660325813.png?resizew=327)
2016·湖南邵阳·中考真题 查看更多[6]
2016年初中毕业升学考试(湖南邵阳卷)数学(已下线)2年中考1年模拟 第五篇 图形的变化 专题29 相似与位似(已下线)【万唯原创】2017年河北省中考数学-试题研究-练习册第七章5+6(已下线)【万唯原创】2017年河北省中考数学-面对面-练习册第七章5(已下线)24.3(2) 三角形一边的平行线-2020-2021学年九年级数学上册《课时同步练》(沪教版)(已下线)【万唯原创】2017年山西-面对面练习册-第七章5上
更新时间:2016-12-06 13:06:59
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真题
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【推荐2】如图,
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名校
【推荐2】如图1,在菱形
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【推荐2】知识背景:恩施来凤有一处野生古杨梅群落,其野生杨梅是一种具特殊价值的绿色食品.在当地市场出售时,基地要求“杨梅”用双层上盖的长方体纸箱封装(上盖纸板面积刚好等于底面面积的2倍,如图)
实际运用:如果要求纸箱的高为0.5米,底面是黄金矩形(宽与长的比是黄金比,取黄金比为0.6),体积为0.3立方米.
①按方案1(如图)做一个纸箱,需要矩形硬纸板
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