若等腰△ABC(AB=AC),能用一刀剪成两个等腰三角形,则∠A=______.
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若等腰△ABC(AB=AC),能用一刀剪成两个等腰三角形,则∠A=______. |
答案
(1)当顶角为锐角时, ①∵剪后AB=AC,AD=BD=BC,∠C=∠ABC=∠BDC=2∠A. ∴∠A+∠C+∠ABC=5∠A=180° ∴∠A=36° ②当AB=AC,AD=BD,BC=CD时 可求出∠A=;
(2)当顶角为钝角时, ∵剪后AB=AC,AC=CD,BD=AD,∠C=∠B=∠BAD=∠ADC=∠DAC ∴∠B+∠C+∠BAD+∠DAC=5∠C=180° ∴∠C=36° ∴∠BAC=108°
(3)当顶角为直角时, ∵剪后AB=AC,CD=AD=BD,∠B=∠C=∠CAD=∠BAD=45° ∴∠CAB=90° 所以填∠A为36°、或90°或108°.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025123024-81963.png) |
举一反三
如图,在△ABC中,AB=AC,点D为BC边的中点,∠BAD=20°,则∠C=______.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025122952-56269.png) |
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![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025122933-41668.png) |
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![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025122920-24873.png) |
已知:如图,在△ABC中,AD⊥BC,垂足为点D,BE⊥AC,垂足为点E,M为AB边的中点,连接ME、MD、ED. (1)求证:△MED为等腰三角形; (2)求证:∠EMD=2∠DAC.
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025122857-34084.png) |
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![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025122855-61265.png) |
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