如图,点B、F、C、E在同一直线上,
、
相交于点G,
,垂足为B,
,垂足为E,且
,
.
(1)求证:
;
(2)若
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a679040c4d556723e482bacbab41356d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf4dc4d7d30af1cdce660795e0fd7d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5322a78b02c2bc387ea7dce3e9461974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c244edbf77fbb8e9c017515e370c5c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c55ee522f41c43253050e92b3c8de31.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/5/52e6ca11-1885-46ff-8b87-3a3d873d6c58.png?resizew=173)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac61f3477e623aa4f924a82bd7a06ce4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d57d36b474e1a24c90489254d5516f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080bffe5d8683cc24d993d0939a9fc74.png)
更新时间:2023-12-04 16:39:55
|
相似题推荐
解答题-证明题
|
适中
(0.65)
【推荐1】如图1,已知∠ACD是
ABC的一个外角,我们容易证明∠ACD=∠A+∠B,即:三角形的一个外角等于与它不相邻的两个内角的和.那么,三角形的一个内角与它不相邻的两个外角的和之间存在怎样的数量关系呢?
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/3/31abaedc-aad9-4171-b5b9-cb2db49ac814.png?resizew=585)
(1)尝试探究:如图2,已知:∠DBC与∠ECB分别为
ABC的两个外角,则∠DBC+∠ECB-∠A 180°.(横线上填<、=或>)
(2)初步应用:如图3,在
ABC中,BP、CP分别平分外角∠DBC、∠ECB,∠P与∠A有何数量关系?请利用上面的结论直接写出答案:∠P= .
(3)解决问题:如图4,在四边形ABCD中,BP、CP分别平分外角∠EBC、∠FCB,请利用上面的结论探究∠P与∠BAD、∠CDA的数量关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/3/31abaedc-aad9-4171-b5b9-cb2db49ac814.png?resizew=585)
(1)尝试探究:如图2,已知:∠DBC与∠ECB分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
(2)初步应用:如图3,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
(3)解决问题:如图4,在四边形ABCD中,BP、CP分别平分外角∠EBC、∠FCB,请利用上面的结论探究∠P与∠BAD、∠CDA的数量关系.
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】(1)如图①,在△ABC中,∠B=60°,∠C=80°,AD平分∠BAC.求证:AD=AC;
(2)如图②,在△ABC中,点E在BC边上,中线BD与AE相交于点P,AP=BC.求证:PE=BE.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/4/da53f6fb-49e0-4977-b3cb-009ffd56bd43.png?resizew=169)
(2)如图②,在△ABC中,点E在BC边上,中线BD与AE相交于点P,AP=BC.求证:PE=BE.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/4/da53f6fb-49e0-4977-b3cb-009ffd56bd43.png?resizew=169)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/4/e5e64210-5491-4fc7-88cc-5c198f0448ab.png?resizew=170)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐3】【问题呈现】小强在一次学习过程中遇到了下面的问题:
如图①,在
与
中,
,
,
.
求证:
.
![](https://img.xkw.com/dksih/QBM/2022/5/31/2991227185659904/2992254938054656/STEM/0793e26e-23b5-4f59-a536-07fcc562630d.png?resizew=514)
【方法探究】以下是小强的方法:
证明:如图②,延长AC到点G,使
,连结BG.
∵
,∴
∴
.
接下来只需证明
,进而就能得出
.
请你补全余下的证明过程.
【方法总结】从上面的方法可以看出,通过“化折为直”,不仅可以构造等腰三角形,还可以得到角的倍、半关系,可谓一举两得.
【方法应用】如图③,在
中,
,
,延长BC到点D,使
,点E在边AC上,连结DE,当
时,
的大小为______°.
![](https://img.xkw.com/dksih/QBM/2022/5/31/2991227185659904/2992254938054656/STEM/5c50a5ed-fe0a-4816-ab4c-45c75f056735.png?resizew=331)
【拓展延伸】如图④,在
中,
,
.若
,
求边AC的长.(精确到0.1)
[参考数据:
,
,
]
如图①,在
![](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/0a510a3eb906b3ef0760b0d1723d11ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439fbb8974a5f907205d26b47b420bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/938284ee5a3740e1d1300a1655dab080.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f350f46b696aa57a5eb5d01df36c5b1.png)
![](https://img.xkw.com/dksih/QBM/2022/5/31/2991227185659904/2992254938054656/STEM/0793e26e-23b5-4f59-a536-07fcc562630d.png?resizew=514)
【方法探究】以下是小强的方法:
证明:如图②,延长AC到点G,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77b6e2a527a14809aa4b196633ea74b.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f77b6e2a527a14809aa4b196633ea74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4319871d9b2914c2a9c60ee3e63e093e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2be0c86eff5028a1a8a2b198456f76.png)
接下来只需证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be7105e6b69a71072c5ae591c3d7c671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f350f46b696aa57a5eb5d01df36c5b1.png)
请你补全余下的证明过程.
【方法总结】从上面的方法可以看出,通过“化折为直”,不仅可以构造等腰三角形,还可以得到角的倍、半关系,可谓一举两得.
【方法应用】如图③,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a355958abf7dc0f2eb949584cb87907b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c859203ce0c1a56900a4cca89c8d4ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f213621229843639780aae87fa29584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33eae5c2324a0fd776f45f8578d25ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5d3f1c7f7ffdf572978468d5a3adde.png)
![](https://img.xkw.com/dksih/QBM/2022/5/31/2991227185659904/2992254938054656/STEM/5c50a5ed-fe0a-4816-ab4c-45c75f056735.png?resizew=331)
【拓展延伸】如图④,在
![](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/41bef89ac0dd5ae192cd9c7222d5041b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165edbc514e343b88731a06cfbbf49c3.png)
求边AC的长.(精确到0.1)
[参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79cbbadc8d9e4d8941bfcbee62aa19d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea639f70d05c5abcf49151be1740fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6f7c6e1fa6e15048866daa8bdadd53e.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐1】已知,AB∥CD,点 E 为射线 FG 上一点.
(1)如图 1,若∠EAF=30°,∠EDG=40°,则∠AED= °;
(2)如图 2,当点 E 在 FG 延长线上时,此时 CD 与 AE 交于点 H,则∠AED、∠EAF、∠EDG之间满足怎样的关系,请说明你的结论;
(3)如图 3,DI 平分∠EDC,交 AE 于点 K,交 AI 于点 I,且∠EAI:∠BAI=1:2,∠AED=22°,∠I=20°,求∠EKD 的度数.
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,
.
;
(2)若
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c993e3e2585171fd72aab1f6aa72dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4009aa13093cc3865dcd51b371892160.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628d3f1b25988307689871b222e28d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a2db6311e228ed33b6c71d0a5918cf.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐1】如图,在△ABC中,AD平分∠BAC,DE⊥AB于E,DF⊥AC于点F,BD=CD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/c5f049b7-c523-4d34-a591-402b1ab2fc0a.png?resizew=188)
(1)求证:DE=DF;
(2)判断△ABC的形状并证明.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/c5f049b7-c523-4d34-a591-402b1ab2fc0a.png?resizew=188)
(1)求证:DE=DF;
(2)判断△ABC的形状并证明.
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,在
中,
,
平分
,交
于点
,
于
,点
在
上,且
.
(1)求证:
;
(2)若
,
,求
的长.
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c38dfd14dde969702dff97ef2270f9.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47256452f509ebc7ff090ca5cfc88142.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/12/91b28821-8f2a-498e-a094-73f25d44586a.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc94684ad41884468d9f5a22853ebcc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34db5860990e51ba31edc8cdd077c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f21d8e7af78693e5da7957c8034e8bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
您最近一年使用:0次