如图,在平行四边形
中,已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/c80458cc-d98e-4435-84e7-e212799de64a.png?resizew=174)
(1)实践与操作:作
的平分线交
于点
,在
上截取
,连接
.(要求:尺规作图,保留作图痕迹,不写作法)
(2)求证:四边形
是菱形.(在下列横线上补全推理过程或推理依据)
证明:四边形
是平行四边形,
∴
,
∴ ① ,( ② )
∵
平分
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb88f0386fc3ae7d108e79305e2e712f.png)
∴ ③
④
由(1)得:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027f82d255ca6058000c9683a6cffd7b.png)
又∵ ⑤
∴四边形
是平行四边形,( ⑥ )
∵ ⑦
∴四边形
是菱形.( ⑧ )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb6694f3443cc5f4d09948679251b61.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/10/c80458cc-d98e-4435-84e7-e212799de64a.png?resizew=174)
(1)实践与操作:作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.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://staticzujuan.xkw.com/quesimg/Upload/formula/14833dbeed409b33acd4c9071fd0be36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
证明:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
∴ ① ,( ② )
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb88f0386fc3ae7d108e79305e2e712f.png)
∴ ③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3006396a74ac1f3da6243cdf180e51.png)
由(1)得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14833dbeed409b33acd4c9071fd0be36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027f82d255ca6058000c9683a6cffd7b.png)
又∵ ⑤
∴四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
∵ ⑦
∴四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
更新时间:2023-12-10 08:32:18
|
相似题推荐
解答题-证明题
|
适中
(0.65)
【推荐1】已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/17/03bcac5e-dd6e-46a0-a50c-424c41795de3.png?resizew=534)
(1)如图1,求证:
;
(2)如图2,点F在
内且在
之间,
平分
平分
,请猜想
与
的数量关系并证明;
(3)如图3,点M在
上,点N在
上,点E是
上方一点,点G在
之间,连接
的延长线
平分
平分
,若
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/17/03bcac5e-dd6e-46a0-a50c-424c41795de3.png?resizew=534)
(1)如图1,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29dee8fc6117283d4b93aeca13a345e.png)
(2)如图2,点F在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4598486f8c5ac28b1165b76e78105979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28d2790a97390935125aa897417f970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d218e8b13cf2f0119ac9a2c78b9dfbfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3db3f03c05b28155f9c0d31abfab198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e8c257f5615d30660cef4157c6b273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a852c13de65877be1f43ac1f88f179d7.png)
(3)如图3,点M在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28d2790a97390935125aa897417f970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0361b5b6b7473e7843e246438db5374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5ed83a3da831ee1a28988a403cca41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d0d739401e5175ea64194632084088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06c67913f1ebfc1f2b7f0f0c9a0e7c99.png)
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您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图①,已知:
平分
,
平分
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/13/87d51029-5e25-4f5e-9258-9b5ed7c2ce38.png?resizew=550)
(1)求证:
;
(2)若射线
、
分别在
、
内部,且
,如图②.当
时,直接写出
的值;
(3)
是直线
上一动点(不与点
重合),
平分
交直线
于点
.设
,直接写出
的度数(用含
的代数式表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246a86f34603eaf2e6a948681b831b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a72dfbf0138a611174c36ce077e0c47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5952817b5eff5ac44229114737c6fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/13/87d51029-5e25-4f5e-9258-9b5ed7c2ce38.png?resizew=550)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
(2)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cfc2771aa0d5b97d2297f8a26a6f6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d19f963f7c803bcfcbb265ec6d4304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019e6026da0b4c908b4d2b9e6a84c375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d96549ae243eb2f8f4e3ce6135a2f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b77651db1804d55f9616b9a732f0cd.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48689c8d5e36b00d476dcfd2ac3d6024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解答题-作图题
|
适中
(0.65)
名校
【推荐1】如图“
字形”
,
,
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/6/cd726ab2-d224-4821-b450-576590bdc8e9.png?resizew=172)
(1)作
的角平分线
,交
于点
,作出线段
的中点
.(要求:尺规作图,保留作图痕迹,不必写出作法)
(2)利用三角尺过点
作
,垂足为
,以
为圆心,
长为半径作圆.
①判断
与直线
的位置关系,并说明理由;
②连接
,若
,
,求
的半径.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c9280aa6e42fb14f08109805517476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/6/cd726ab2-d224-4821-b450-576590bdc8e9.png?resizew=172)
(1)作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb8eca20ce2c918ea4034ea15210c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)利用三角尺过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d1614b23fa6632b914f9a42fdfb8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
①判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989dc4af481c6133824200942b9e5c8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
②连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e46494a6657c85a9e35d8a07cdb81a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc848db282db12957acad1e0983d2705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/989dc4af481c6133824200942b9e5c8d.png)
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解答题-作图题
|
适中
(0.65)
【推荐2】如图,点A 和B在反比例函数
的图象上,
轴于点C,且
的面积为
,点A的纵坐标为1,射线
与x轴负半轴的夹角为
.
(1)求反比例函数的解析式和点A的坐标.
(2)请用无刻度的直尺和圆规作出
的平分线(要求:使用2B铅笔作图,不写作法,保留作图痕迹).
(3)过点A作
交
的平分线于点D,若
,直接写出点D的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa915a60a2d6e535369715ba84015b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05de5eef286a1b48012246c0cf88a1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7ffcd1925a2b1259221c6a476152f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/1/1c10e4a3-b4e9-4506-9f97-c7a5661b7183.png?resizew=167)
(1)求反比例函数的解析式和点A的坐标.
(2)请用无刻度的直尺和圆规作出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
(3)过点A作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfde2b6b26097412f142ff4414367454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33bc4de3f4e1b433b91d2bf22740209.png)
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解答题-证明题
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适中
(0.65)
【推荐1】如图,在▱ABCD中,点E,F,G,H分别是AB,BC,CD,DA上的点,且满足AE=CG,BF=DH.
试证明:EG,FH互相平分.
试证明:EG,FH互相平分.
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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,在平行四边形
中,点E、F、G、H分别在边
上,且
,连接
.
;
(2)若
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b589ca985b32e60ea2e39fe58d4ac9d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642cbdc8b2f38e13ff85ec99d8aa5cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb08ca42f5d3f7402a67d3d68cd6fb4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997a05c024e687e6b7f4e0f2b7e5bff7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c3f8fe900e249c4e3f8a3cc0cb7f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100fefbb32028bef119d69ee278684aa.png)
您最近一年使用:0次
解答题-证明题
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适中
(0.65)
名校
【推荐1】在
中,对角线
、
相交于点
,
过点
且与
,
分别相交于点
,
.
;
(Ⅱ)如图②,若
,垂足为
,求证:四边形
是菱形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf2e3236ea30ee2c37928b98041f13a.png)
(Ⅱ)如图②,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a3fc19d03bca6562f40039a2e124b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2330c01a4d2b5b20f106e3e48834d5c0.png)
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解答题-证明题
|
适中
(0.65)
【推荐2】如图,在平行四边形ABCD中,以A为圆心,AB长为半径画弧交AD于点F;再分别以B、F为圆心,大于
的相同长为半径画弧,两弧交于点P;连接AP并延长交BC于点E,连接EF,则四边形ABEF是菱形.
(1)求证:四边形ABEF是菱形;
(2)若菱形ABEF的周长为8,
,求∠C的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36657d9f8560180cbda94326e8a9cf53.png)
(1)求证:四边形ABEF是菱形;
(2)若菱形ABEF的周长为8,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941eba4dbc1094107e1eeb02c8d8cd56.png)
![](https://img.xkw.com/dksih/QBM/2020/3/3/2411446420430848/2411644431826944/STEM/61cbe3176d994783b3b3108437609630.png?resizew=175)
您最近一年使用:0次