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【332229】1.1.2 菱形的性质与判定(2)

时间:2025-01-21 12:29:36 作者: 字数:1417字
简介:







菱形的性质与判定

解答题

1.已知:如图,在 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 中,DBC边上一点, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ABE <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ACF,且 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 求证:四边形AEDF是菱形.

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>

2.已知:如图,在菱形ABCD中,EF分别是BCCD上的点, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,求 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 的度数.

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>

3.已知:如图,四边形ABCD是菱形,ACBD是对角线, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> .求证: <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>

4.如图,菱形ABCD的对角线交于点 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,求菱的高.

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>

5.如图,在菱形ABCD中, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 相交于点O,且 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,若 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,求菱形ABCD的面积.

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>

6.如图,在 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ABCD中, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,把AB向两方延长,使 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,连结CEDF,请问CEDF有怎样的位置关系,并证明你的结论.

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>



7.把两条宽度相同的纸条交叉重叠放在一起,如图,重叠部分ABCD是什么四边形?度证明你的结论?

 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>




参考答案

1 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 四边形 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 是平行四边形,又 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 平行四边形 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 是菱形.

2.连结 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 是等边三角形, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,又可证 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 是等边三角形, <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>

3.由 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,可知菱形的高等于边长的一半. <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>

49.6cm

5 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>

6 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,连结MN,可证得 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,则 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,同理 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,由 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,且 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 可知四边形 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 是平行四边形,又 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,可知四边形 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 是菱形,所以 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>

7 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 是菱形,作 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> Q,由于两纸条的宽度相等,所以 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,则 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,则 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a>  <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> ,又由四边形是平行四边形可知 <a href="/tags/386/" title="性质" class="c1" target="_blank">性质</a> <a href="/tags/868/" title="判定" class="c1" target="_blank">判定</a> <a href="/tags/899/" title="菱形" class="c1" target="_blank">菱形</a> 是菱形.