1 . 如图,要测量池塘两岸M,N两点间的距离,可以在直线
上取A,B两点,再在池塘外取
的垂线
上的两点C,D,使
,过点D再画出
的垂线
,使点E与A,C在一条直线上.若此时测得
,
,
,则池塘两岸M,N两点间的距离为________ m.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a16dc02090b6e9263555061f14fbc8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad0265332a459a48a203cb89d3703e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa611a7d20a31605dbf551fed5cb91a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893e050f628daa7a3439eff77e481ad0.png)
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2 . 如图,
和
交于点O,
,
,求证:
.
![](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/0fec9e3bf7ff287df2cbdff8addfaf5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38aa46b02f08fca3728f1158ea0047fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50834e39c4e028e0fc303b94d571923.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/e9b8e42d-6da6-4604-86d7-ae81c97a2240.jpg?resizew=154)
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3 . 如图,为测量河宽
,小军站在河岸的O处调整好自己的帽子,使视线恰好擦着帽舌边缘看到对面的Q处,然后沿
所在直线后退到B处(保持之前的姿势),这时他的视点恰好落在O处,同时他让小华测量他此时所站的B处与O处之间的距离为
.你能帮忙算出河宽
吗?请说明理由.
AI
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f631cfdf4666db95beb923072ced8d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/23/79dac300-e74a-4e36-93ae-8ebc4274b948.png?resizew=280)
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4 . 如图,在
中,
是
边上的中线,
于点E,
交
的延长线于点F.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/17/8671e9ca-0870-489b-a706-e2e92fb07045.png?resizew=162)
(1)求证:
;
(2)若
=16,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/497846628a41a9bc750a645e045afb47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9d0c688e55286443c9974797fc647f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/17/8671e9ca-0870-489b-a706-e2e92fb07045.png?resizew=162)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533f1f6ead0d794bb7c70cce9173d4a5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/577250c86a14c7a2990bf9852c7213d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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5 . 如图,要测量河岸相对的两点A、B之间的距离.已知
垂直于河岸
,现在
上取两点C、D,使
,过点D作
的垂线
,使A、C、E在一条直线上,此时,只要测出
的长,即可求出
的长,此方案依据的数学定理或基本事实是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4eccda4edcee29a5f15609e85106df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4eccda4edcee29a5f15609e85106df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7305de9211785b826823153897b17517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4eccda4edcee29a5f15609e85106df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8946331b0a9d86e1a9c78797f3021455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8946331b0a9d86e1a9c78797f3021455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/9c6c4a40-702a-4a2b-91f7-acecc2091d35.png?resizew=163)
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2023-12-12更新
|
61次组卷
|
2卷引用:山东省滨州市无棣县2023-2024学年八年级上学期期中数学试题
6 . 如图,在
中,
,
,过点C作
,且
,则
的面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/61579d95-ec82-43dc-8276-e04a2d72227f.png?resizew=146)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfa14df2e34162f35f421f2ae598cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffc2a946e72f26a8af584d8ead3a396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/61579d95-ec82-43dc-8276-e04a2d72227f.png?resizew=146)
A.4 | B.6 | C.7 | D.8 |
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7 . 如图,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7187a174aa44ba9c553c47c227c530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4354365ca0929f8a606ed0bf341e4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/7c62d706-5c63-4576-8ef9-714aa2d8880c.png?resizew=132)
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2023-12-11更新
|
119次组卷
|
2卷引用:江苏省连云港市灌云县2023-2024学年八年级上学期期中数学试题
8 . 如图,点
在
边上,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/ba05a1ce-8dc4-490b-89b9-88b18760b77d.png?resizew=238)
(1)求证:
;
(2)若
,求
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb2e124dcbd798dcf5b67fb447868ed.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/ba05a1ce-8dc4-490b-89b9-88b18760b77d.png?resizew=238)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528fa89492fc43b433557508fff7a19a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9c14d7ac0501707e8d6eb48a956faa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3e081637bcea5368cc72370bae283b.png)
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2023-12-10更新
|
216次组卷
|
2卷引用:辽宁省葫芦岛市连山区2023-2024学年八年级上学期期中数学试题
名校
9 . 如图,四边形
中,M是
的中点,
过点M,与
交于点E,与
的延长线交于点F,请在下列四个条件中:
①
;②
;③
;④M是
的中点.
选出一个作为已知条件,推出
.并证明.(写出一种即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/24/0e74c96c-c9ec-489d-81f8-421dac42d1aa.png?resizew=173)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4a94e65672e52bac3e6c927b0a66d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
选出一个作为已知条件,推出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339ffab343ccede8c9bf52da262396e9.png)
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10 . 如图,小明与小敏玩跷跷板游戏,如果跷跷板的支点O(即跷跷板的中点)至地面的距离是
,当小敏从水平位置
下降
时,小明离地面的高度是__________ cm.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd507983ffb3f77f6349aa1554b5ac48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19daa2b38e3a52bd7096d235c843110.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/3ed75642-8c91-4355-bb56-2f0b6e8f83ed.jpg?resizew=142)
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