如图,已知线段
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/6/af07d832-703e-4597-8c4c-d68c380a4fc8.png?resizew=165)
(1)画图:延长线段
至
,使
,取线段
的中点
;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d42e97eee705d164e6ac6de9ecd6d1f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/6/af07d832-703e-4597-8c4c-d68c380a4fc8.png?resizew=165)
(1)画图:延长线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe44ff9f829f6c034682572ad00e366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f01c4faacedfe56f5127d6c0cc63cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
更新时间:2020-03-19 18:17:59
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名校
【推荐2】如图,
,C是
上一点,且
,D是
的中点,E是
的中点,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9040c9795e7132ebf65ede1f98c4d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e78e09d194bf11cc12858fd22d58b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/2021/12/14/2872171261550592/2872514329485312/STEM/7cbe5b0d-4c13-4f45-bbd6-ecbdf94d7345.png?resizew=282)
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解答题-作图题
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【推荐1】补全解题过程:
已知:如图,点
在线段
上,
,点
是线段
的中点.
,求线段
的长.
解:∵点
是线段
的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
∴
______=______
∵
______
∵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846071242f981289741ad19f4e7190cf.png)
∴
______![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
∴
______
∴
______
已知:如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846071242f981289741ad19f4e7190cf.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/55c24a968c73e960698a572ab01e3698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
解:∵点
![](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/55c24a968c73e960698a572ab01e3698.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9e89617f00be03e2c605992347d355.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846071242f981289741ad19f4e7190cf.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae248960d8c1677cf948f8251275e863.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4865ca63bdaff99beda4625dbe289b.png)
![](https://img.xkw.com/dksih/QBM/2022/1/9/2890854675677184/2891470401413120/STEM/92e440d6-b361-42db-afdb-1bba9664f296.png?resizew=245)
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【推荐2】老师留给学生这样一道数学巩固性作业:如图线段
,点O是线段
上一点,C,D分别是线段
、
的中点.请你帮忙解决以下问题.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/23/a4ce61b4-5914-4a26-a8c7-e788f496c08e.png?resizew=323)
(1)求线段
的长.
(2)小军完成作业(1)后,在反思过程中突发奇想:若把“点O是线段
上一点”改为“点O是线段
延长线上一点”,其他条件不变,如何画图?线段
的长又是多长?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/23/a4ce61b4-5914-4a26-a8c7-e788f496c08e.png?resizew=323)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)小军完成作业(1)后,在反思过程中突发奇想:若把“点O是线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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【推荐1】已知点
在线段
的延长线上,点
,
分别是
,
的中点.
(1)如图,若
,则线段
_______;
_______;
_______;
_______.(直接写出结果)
(2)若
其它条件不变,求线段
的长.(用含
的式子表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/17/0eea9799-2d6e-41ae-b8bb-fe9a00887e9b.png?resizew=271)
(1)如图,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8dc33f016fdff2ebeb409d6db09a006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae248960d8c1677cf948f8251275e863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3ae0ac1cd4e5221eb8be9463c166a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0825285395b846c4a159d926fd25ebcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2b3247afa684b10c8e1da99cf33d5b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5d1cc92c56c67fa09ed4ba754ccfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解答题-作图题
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【推荐2】补全解题过程.
如图所示,点
是线段
的中点,延长线段
至点
,使
,若
,求线段
的长.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/e7157b96-099d-4f21-9227-f4c4e7e4d863.png?resizew=224)
解:∵点
是线段
的中点(已知)
∴
______(_______________________)
∵
(已知)
∴
______.
∵延长线段
至点
,使
(已知)
∴
______.
∴
______
______.
如图所示,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc407329b26b97f085ddccd91c9565dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/e7157b96-099d-4f21-9227-f4c4e7e4d863.png?resizew=224)
解:∵点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
∵延长线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc407329b26b97f085ddccd91c9565dc.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978d92edf0c4c1ef8620c17df75d35e.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5d678ec42846e1d28301e3bfd4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2546dac5dcd3041036ab1ae1b2978885.png)
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