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【330103】18.2.1 第1课时 矩形的性质1

时间:2025-02-08 16:45:52 作者: 字数:2948字

18.2 特殊的平行四边形

18.2.1 矩形

1课时 矩形的性质


1.我们把__________ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 做矩形.

2.矩形是特殊的____________,所以它不但具有一般________的性质,而且 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 还具有特殊的性质:(1_________;(2___ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> ________

3 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 矩形既是______图形, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 又是________图形,它有_______条对称轴.

4 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 如图1所示,矩形ABCD的两条对角线相交于点O,图中有_______个直角三角形,____个等腰三角形.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>

5.矩形的两条邻边分别是 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>2,则它的一 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 条对角 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 线的长是_____ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> _

6.如图所示,矩形ABCD的两条对角线相交于点O,若∠ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> AOD <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> =60°OB=4DC=____ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> ____

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>

7.矩形具有而一般平行四边形不具有的性质是( )

A.对角线相等 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>  <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> B.对角相等 C.对边 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 相等 D.对角线互相平分

8.若矩形的对角线长为4cm,一条边长为2cm,则此矩形的面积为( )

A8 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> cm2 B4 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> cm2 C2 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> c <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> m2 D8cm2

9.如图2所示,在矩 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>ABCD中,∠DBC=29°,将矩形沿直线BD折叠,顶点C落在点E处,则∠ <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> ABE的度数是( <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>

A <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 29° B32° C22° D61°

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>

10.矩形ABCD的周长 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>56,对角线ACBD交于点O,△ABO与△BC <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> O的周长差为4AB的长是( )

A12 B22 C16 D26

11.如图3所示,在矩形ABCD中,EBC的中点, <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> AE=AD=2,则AC的长是( )

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> A <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> B4 C2 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> D <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>

12.如图所示,在矩形 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> ABCD中,点EDC上,AE <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> =2BC,且A <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> E=AB,求∠CBE的度数.


 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>





13.如图所示,在 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 矩形ABCD中,对角线ACBD交于点O,过顶点CCE∥BD,交A孤延长线于点E,求证:AC=CE

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>


 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>



14.如图所示,在矩形ABCD中,AB=8AD=10,将矩形 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 沿直线AE折叠,顶点D恰好落在BC边上的点F处,求CE的长.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>







15.如图所示,在矩形ABCD中,AB=5cmBC=4cm,动点P1cm/s的速度从A点出发,经点DC到点B,设△ABP的面积为scm <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 2),点P运动的 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 时间为ts).

1)求 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 当点P在线段AD上时,st之间的函数关系式;

2)求当点P在线段BC上时,st之间的函数关系式;

3)在同一坐标系中画出点P在整个运动 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 过程中st之间函数关系的图 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 像.

 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>




答案:

1.有一个角是直角的平行四边形

2.平行四边 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 形,平行四边形

1)矩形的四个角都是直角 (2)矩形的 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 对角线相等

3.中心对称,轴对称,2 444 53 64 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a>

7A 8B <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 9B 10C 11D 12 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> 15°

13.证四边形BDCE是平行四边形,得CE=BD=AC

143 15 <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> .(1s= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> t 2s= <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> - <a href="/tags/16/" title="课时" class="c1" target="_blank">课时</a> <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/900/" title="矩形" class="c1" target="_blank">矩形</a> t+35 3)略