如图,在
中,
,
是
的角平分线,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/2f6b9251-68e8-4eaf-a025-701192e184a1.png?resizew=142)
(1)尺规作图:过点D作
于点E.(保留作图痕迹,不写作法)
(2)在(1)所作的图形中,若
,点F为线段
上一点,且
,连接
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/2f6b9251-68e8-4eaf-a025-701192e184a1.png?resizew=142)
(1)尺规作图:过点D作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
(2)在(1)所作的图形中,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377b5f7197e5bd1afeea4d931307956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0cee0f36dc452e58086832c0152b641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441dec590b47adc3678a291a3ec89a4a.png)
更新时间:2024-04-07 15:27:35
|
相似题推荐
解答题-作图题
|
适中
(0.65)
名校
【推荐1】下面是小明设计的“在已知三角形的一边上取一点,使得这点到这个三角形的另外两边的距离相等”的尺规作图过程:
已知:△ABC.
求作:点D,使得点D在BC边上,且到AB,AC边的距离相等.
作法:如图,
作∠BAC的平分线,交BC于点D.则点D即为所求.
根据小明设计的尺规作图过程,
(1)使用直尺和圆规,补全图形 (保留作图痕迹);
(2)完成下面的证明.
证明:作DE⊥AB于点E,作DF⊥AC于点F,
∵AD平分∠BAC,
∴ = ( ) (填推理的依据) .
已知:△ABC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/6/ea77d6e1-95a7-4af9-ae2d-c94e8ff2f4ba.png?resizew=187)
求作:点D,使得点D在BC边上,且到AB,AC边的距离相等.
作法:如图,
作∠BAC的平分线,交BC于点D.则点D即为所求.
根据小明设计的尺规作图过程,
(1)使用直尺和圆规,补全图形 (保留作图痕迹);
(2)完成下面的证明.
证明:作DE⊥AB于点E,作DF⊥AC于点F,
∵AD平分∠BAC,
∴ = ( ) (填推理的依据) .
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解答题-证明题
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适中
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【推荐2】如图,已知
中,
的平分线
和边
的垂直平分线
相交于点
过点
作
交
的延长线于点
,
于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94171ac0660560f6e08515879e27ed1c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/23025f30-763c-49bb-9898-ab6714e9b1c6.png?resizew=202)
求证
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239c514ff4ff20f8bb09df311978d504.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c65edad25ddd666cdce0d7e5afefc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b28f28ced0531d1df34fcf04c6c67f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3ad66cf49d46fe39be15f5c23eec68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761a77e11e1e45c2a8b2d34d22cf8e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7ad8d177fc4dcb983c5952ad5533b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94171ac0660560f6e08515879e27ed1c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/6/23025f30-763c-49bb-9898-ab6714e9b1c6.png?resizew=202)
求证
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239c514ff4ff20f8bb09df311978d504.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0465f92c661cc052b04f0d647be797.png)
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解答题-证明题
|
适中
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【推荐3】【综合与实践】
问题情境:
如图1,在
中,
,
为钝角,点D是
的中点,
于点E,
于点F.试判断线段
与
的数量关系,并说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/12/ee3779a8-aee6-40b6-820a-70e5b6fcad9d.png?resizew=606)
探究展示:
小宇同学展示出如下正确的解法:
解: 1 (填写
和
的数量关系),理由如下:
点D是
的中点,
是
边上中线,
,
是
的角平分线.( 2 )(填写结论依据)
,
,
.
反思交流:
(1)完成上面解题过程的两个填空:①:____________________;②____________________;
(2)利用上述结论请继续探究线段
与
的数量关系,并说明理由;
(3)如图2,在图1的条件下,点M是射线
上一点,作
,射线
交线段
于点N,求线段
、
和
之间的数量关系,并说明理由.
问题情境:
如图1,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761a77e11e1e45c2a8b2d34d22cf8e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/12/ee3779a8-aee6-40b6-820a-70e5b6fcad9d.png?resizew=606)
探究展示:
小宇同学展示出如下正确的解法:
解: 1 (填写
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e24c2bdad41127f07c6639a357d2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4046f62f73ca345f5ad182fc0c71e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e24c2bdad41127f07c6639a357d2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ced2c289548afacf525c6e59f204fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6474284422de867b608967587cc28db9.png)
反思交流:
(1)完成上面解题过程的两个填空:①:____________________;②____________________;
(2)利用上述结论请继续探究线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
(3)如图2,在图1的条件下,点M是射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b7c9621d5fd6a1b121390c890d8138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
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解答题-作图题
|
适中
(0.65)
【推荐1】如图,在
中,
.
边上找一点P,使得点P到点A和点B的距离相等;(要求:不写作法,保留作图痕迹,使用
铅笔作图)
(2)在(1)的条件下,若
,
,则
的周长是___________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/772562a411cb35b12e8a5878ddaa9de1.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657921f28d9ebc92f154ac16d3599b3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b13964019381c4cd9de05f95c4261b.png)
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解答题-作图题
|
适中
(0.65)
【推荐2】(1)如图(1),在
中,分别作
边上的高和中线,请用无刻度的直尺完成作图(保留作图痕迹);
![](https://img.xkw.com/dksih/QBM/2020/5/21/2467537496580096/2468208770162688/STEM/64d16d072a634952aedc5938cdc0f94d.png?resizew=220)
(2)如图(2),以
为旋转中心,将
顺时针旋转
度,得到
请用无刻度的直尺作出
(保留作图痕迹).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2020/5/21/2467537496580096/2468208770162688/STEM/403824a887f54a4aad02832fb43ed7dd.png?resizew=238)
![](https://img.xkw.com/dksih/QBM/2020/5/21/2467537496580096/2468208770162688/STEM/64d16d072a634952aedc5938cdc0f94d.png?resizew=220)
(2)如图(2),以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754fb8e4334ffd2f38d69ce4c07c0d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa75169dc974aaf9052f2e12b91adb9e.png)
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