如图,在平行四边形
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/0cd34d33-53d2-410a-9f21-855091f52895.png?resizew=201)
(1)尺规作图:作
的平分线交
于点
;
(2)在(1)所作图形中,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/8/0cd34d33-53d2-410a-9f21-855091f52895.png?resizew=201)
(1)尺规作图:作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3981e7286d41960daf4e110c1c84e03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)在(1)所作图形中,求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
更新时间:2023-03-06 16:16:02
|
相似题推荐
解答题-作图题
|
适中
(0.65)
【推荐1】尺规作图并完成证明.如图,点
、点
在
外,连接
、
、
,且
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/c18ac4a8-69ac-484b-9df9-6d5feb6793e1.png?resizew=177)
(1)用尺规完成以下基本作图:
作
的平分线
交
于点
,连接
(保留作图痕迹,不写作法);
(2)根据(1)中作图,求证:
;请完善下面的证明过程.
证明:
平分
,
__________.
.
__________.
.
__________.
在
和
中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4465431873b7af17eff38dc15882db.png)
.
__________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6095bae4840bfa80f2468f94b2002d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd44e7b89f25f7242e009653f268d72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01476dfb5970e27f54f742c27b9515f9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/c18ac4a8-69ac-484b-9df9-6d5feb6793e1.png?resizew=177)
(1)用尺规完成以下基本作图:
作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)根据(1)中作图,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42218a68301d770accaaefb96b19f8a.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f85f511236e5645290b9d06984558ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c090e36ff8728bf001253526c65e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cde6b202733e1b638bfdc9027a73df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c090e36ff8728bf001253526c65e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac14a0ce88aeee0bacd62fc4983f872f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6f6270ffb9ba9dcbfc795642e17ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4465431873b7af17eff38dc15882db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ae992ad9bcbc8bef39a3c10d3a0f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
您最近一年使用:0次
解答题-作图题
|
适中
(0.65)
【推荐2】阅读下面材料,完成相应任务:
尺规作图
尺规作图是指用无刻度的直尺和圆规进行作图.无刻度的直尺不具有度量长度的功能,它用来作经过两点的直线,射线或线段.圆规用来画弧,圆规的两脚还可以截取线段或两点之间的长度.尺规作图的关键是确定线与线,线与弧,弧与弧的交点,从而构造出符合要求的图形.
在数学课上,在用尺规作角的平分线时,同学们自主探究出很多不同于教材的作法.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/ab291480-6c0a-449e-b6f8-1cafcb032555.png?resizew=143)
已知:
求作:
的平分线.
小明的作法:如图①,在射线
上取点
,分别以
为圆心,
长为半径画弧,交射线
于点
,连接
交于点
,过点
画射线
,则射线
为
的平分线.
小华的思路:如图②,在
上任取一点
,在
的右侧作射线
,使得
,在射线
上取一点
,使
,过点
画射线
,则射线
是
的平分线.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/2cc60164-fdf8-46eb-9cf6-42fed9058a3e.png?resizew=301)
赵老师因势利导,引导同学们对各种作法进行研究,在感受教材作法简洁的同时体会它们的共同之处,即基于角的轴对称性构造全等三角形,得出两个相等的角.
任务一:小明的作法中,可以得出
,请你写出这一结论所依据的数学定理或基本事实.
任务二:根据小华的思路完成下列问题:
(1)使用直尺和圆规,在图②中补全图形(保留作图痕迹);
(2)根据小华的作法,证明
是
的平分线.
尺规作图
尺规作图是指用无刻度的直尺和圆规进行作图.无刻度的直尺不具有度量长度的功能,它用来作经过两点的直线,射线或线段.圆规用来画弧,圆规的两脚还可以截取线段或两点之间的长度.尺规作图的关键是确定线与线,线与弧,弧与弧的交点,从而构造出符合要求的图形.
在数学课上,在用尺规作角的平分线时,同学们自主探究出很多不同于教材的作法.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/ab291480-6c0a-449e-b6f8-1cafcb032555.png?resizew=143)
已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
小明的作法:如图①,在射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdba36d4c2d4acedbd44d08e4c04127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da58a347512f4fc726cba055312c00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec38bedb55b02c42c1fb552e6cbf7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5557e3f084429321ddea623574d26e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
小华的思路:如图②,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667db777bce5dc053916871fce18ec9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e795d041c170e2a62ff1157becd7f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/2cc60164-fdf8-46eb-9cf6-42fed9058a3e.png?resizew=301)
赵老师因势利导,引导同学们对各种作法进行研究,在感受教材作法简洁的同时体会它们的共同之处,即基于角的轴对称性构造全等三角形,得出两个相等的角.
任务一:小明的作法中,可以得出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675ce3a46689f8f49c18059ed537503.png)
任务二:根据小华的思路完成下列问题:
(1)使用直尺和圆规,在图②中补全图形(保留作图痕迹);
(2)根据小华的作法,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐1】已知,如图,在
中,
,垂足为
,
,点
为
的中点,点
为
上的一点,连接
、
、
,
.
(1)若
,
,求
长;
(2)证明:
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f5dc11efe60b4fd9a13b1d6b83842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1d267eeb09c171c3e847f0597be31c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/13/43031279-77c9-4b21-8e2f-ce3eb466f0a2.png?resizew=189)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bc4c9dd737193f7acce692b23500d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86338536656046e93b53672ade9a78b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fbf0c49f5e6b49f1d524e8777fbb47.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/789d64e81f869818c00f810001b5f5b2.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,已知平行四边形
中,对角线
交点O,E是
延长线上的点,且
是等边三角形.
是菱形;
(2)若
,求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75734017987de5788b6d42b549417e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次