题干

如图,在矩形ABCD中,对角线BD的垂直平分线MN与AD相交于点M,与BD相交于点O,与BC相交于N,连接MN,DN.请你判定四边形BMDN是什么特殊四边形,并说明理由.

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答案(点此获取答案解析)

解:四边形BMDN是菱形.理由如下:

∵四边形ABCD是矩形,

∴AD∥BC,OD=OB,

∴∠MDO=∠NBO,

∵MN是BD的垂直平分线

∴在△MOD与△NOB中,

∴△MOD≌△N

同类题3

阅读理解

    Some parents can't resist the strong desire to help their children play hooky (逃学) for a trip. Five-year-old Erica and her siblings Alex, 9, and Kate, 12, missed school in Denver on Aug. 21, 2017. Their father Mr. Reed took them on a camping trip to Halsey to see the solar eclipse (日食). Kate had told her teachers she'd be absent and Mr. Reed let Erica's and Alex's teachers know, too. But he didn't ask for permission.

    Mr. Reed has loved astronomy since seeing Neil Armstrong walk on the moon on his sixth birthday. He says, “I want my own kids to have a similar kind of wonderment and hope about future discoveries.”

    Parents often dream of traveling with their children to teach them about science, geography and culture. Many teachers support them, as the Reed children's teachers did. Other teachers were angry about the extra work.

    Teacher Amanda says she feels frustrated when parents take students out of school for family trips. If she sends homework, she finds it's often returned incomplete or incorrect, because the absent student didn't hear her explanation in class. Some students suffer anxiety as they struggle to catch up. Research shows that students who are absent often, for any reason—excused or unexcused—performed more poorly in school.

    Garrick agreed to miss five days of school for the Antarctic trip last year as a senior high school student, however. Managing the homework was a challenge, but it helped him gain time management skills. “And the trip is worth the effort,” he says, “sparking his interest in international relations. You can't really put a price on changing your world view,” Garrick says. “That's what travel has done for me. It has changed how I think about things.”