1 . 已知
为方程
的解,
,
(1)求证:
.
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99606defee81cacc6652482953b6818c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911958db7bf41c17393a895b6743fac4.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c4b1b48220a0c16bc22c1dfaa1acc0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33e8fca2d3aa21ff0f7ef6962e66651.png)
您最近一年使用:0次
2 . 已知:底与腰之比为
的等腰三角形为黄金三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/d906e69c-33ad-47c1-87a1-046eb54ce27b.png?resizew=337)
(1)如图1,
即为黄金三角形尺规作图.已知
,求
长为______,
为______.
(2)如图2,即为正五边形尺规作图.求证:五边形
(所作图形)即为正五边形.
(3)请用另一种方法尺规作图作出正五边形.简要叙述作图方法,无需作图.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d393bb07b7140905b85f550519de4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/d906e69c-33ad-47c1-87a1-046eb54ce27b.png?resizew=337)
(1)如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
(2)如图2,即为正五边形尺规作图.求证:五边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
(3)请用另一种方法尺规作图作出正五边形.简要叙述作图方法,无需作图.
您最近一年使用:0次
3 . 如图所示,在
中,点
在
边上,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/a5b4a0d2-1629-4d90-99fb-a6479cb11e05.png?resizew=488)
(1)若
.
①如图1,若
,
,过
作
于点
,直接写出
的值为 ;
②如图2,若
,求
的值.
(2)如图3,已知
为
的角平分线,
,
,直接写出线段
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/a5b4a0d2-1629-4d90-99fb-a6479cb11e05.png?resizew=488)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092f6c8e7e90d46c1ee0457f17daeb4a.png)
①如图1,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629be4a6de577f13c9b0a524e7a5e383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b62ce0cbffa4758c7a0e6fb7ca4d24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c06aa28f4e4ee00cdf3c8e7847225ed.png)
②如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7e75d7342e6f087370d09181b17a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120223970943dc87c216b0860e502254.png)
(2)如图3,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e50f0d02d0bd51ae361d276ed9dea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d035c3a7a6126dabbba817cf0506a78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
您最近一年使用:0次
4 . 求证:数列
中一定有2022的倍数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69719252d1232ef3ce59579f51104c81.png)
您最近一年使用:0次
5 . 若一个直角三角形中两条直角边都是整数,且周长是面积的整数倍,则称其为“
三角形”,则这样的“
三角形”共有______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
6 . 如图,
是横坐标为2的定点,点
在直线
上运动,
,
,当点
从原点
运动到横坐标为2的点
时,点
的运动距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b92a937da50218ce1b0f6b26c03a117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15b82151bff7cc0238d2034a6129f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/f5f510c1-9c5a-40b9-beaa-bdae936ab288.png?resizew=165)
您最近一年使用:0次
7 . 如图,
和
都是边长为2的等边三角形,它们的边BC,EF在同一条直线l上,点C,E重合.现将
沿直线l向右移动,直至点B与F重合时停止移动.在此过程中,设点C移动的距离为x,
为y,则下列结论:
①y始终随x的增大而减小;
②y的最小值为3;
③函数y的图象关于直线
对称;
④当x取不同的数值时,y也取不同的数值.
其中,正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acaca5b9663c6ef657b38830bd07fad5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/5/6564a602-9da0-44d2-acb5-d18098c4a2c5.png?resizew=218)
①y始终随x的增大而减小;
②y的最小值为3;
③函数y的图象关于直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
④当x取不同的数值时,y也取不同的数值.
其中,正确的是( )
A.①② | B.①④ | C.②③ | D.② |
您最近一年使用:0次
8 . 已知矩形ABCD,点E、F分别在AD、DC边上运动,连接BF、CE,记BF、CE交于点P.
,求线段DE的长度;
(2)如图2,若
,求
;
(3)如图3,连接AP,若
,求PB的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3274fa0ba1cc131cf913802f7733001a.png)
(2)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29402df410d36f0e9b938b29f45595b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34892d160c72edfc3d1e3f12adca89f.png)
(3)如图3,连接AP,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1044f5984d06e1d15fc0ef941c283261.png)
您最近一年使用:0次
名校
解题方法
9 . 已知直线
,点
是
之间的一定点,并且P点到
的距离分别是
,B点是
上的一动点,作
,且使
与
交于点
,则以下说法中正确的有____________ .
①三角形
的面积存在最小值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98928d2735c4668d486ba89bde055902.png)
②
存在最大值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46ae27a5beb3517cd2e538cbd139495.png)
③当
时,
的长存在最小值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15752847ab476edec45450680887baa8.png)
④当
时,点P到
的距离为定值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0dd294f8053b5a82d808ee00f924c2.png)
⑤当
时,
与
的夹角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1095c036b49c3327baaa2c3c7f746134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b721afb477b5e952b82ce210a85cc4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
①三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98928d2735c4668d486ba89bde055902.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384b9afcef2d86a87eee0c66f383052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46ae27a5beb3517cd2e538cbd139495.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9605cb0aa53deddc440e97668291eaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15752847ab476edec45450680887baa8.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9605cb0aa53deddc440e97668291eaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0dd294f8053b5a82d808ee00f924c2.png)
⑤当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358b4aa966786b625dd708fd76569da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
您最近一年使用:0次
名校
解题方法
10 . 已知数列
是等差数列,数列
满足
.
(1)求证:数列
是等差数列;
(2)设数列
、
的公差均为
,且存在正整数
,使得
,求
的最大值;
(3)在(2)的条件下,当
取得最大值时,设
,记数列
的前
项和为
,问:是否存在自然数
,使得
成立?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca3c52ce55a45e33576a1f066d13e21.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bfe21c96489cb30c544d49ddb4c1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056a90a2751f04ba5fff3dc5c1d0674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932cf0896df0a5b07d108f21f69be099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b90708f70dc76a877bb52fe17e3208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f183b4291a4d22fe4f704e2a90f31dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b341d1d30b8f27fd936a8c8069afde4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8089bfe21f5dc209ebf6b7f26ce97ab5.png)
您最近一年使用:0次