等腰梯形ABCD中,AD∥BC,AD=DC=AB,BD=BC,求∠A的度数

问题描述:

等腰梯形ABCD中,AD∥BC,AD=DC=AB,BD=BC,求∠A的度数

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∵等腰梯形ABCD∴∠ABC=∠C∵AD=AB∴∠ABD=∠ADB∵AD//BC∴∠ADB=∠CBD∴∠ABD=∠CBD=∠ABC/2∴∠ADB=∠ABC/2∴∠ADB=∠C/2∵BD=BC∴∠BDC=∠C∵AD//BC∴∠C+∠BDC+∠ADB=180°∴∠C+∠C+∠C/2=180°∴...