如图,已知AB‖CD,角1=角B,角2=角D,判断BE与DE的位子关系JJJJJJJJJJJJJJJJJJJJJJJJ

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/03 04:56:29
如图,已知AB‖CD,角1=角B,角2=角D,判断BE与DE的位子关系JJJJJJJJJJJJJJJJJJJJJJJJ

如图,已知AB‖CD,角1=角B,角2=角D,判断BE与DE的位子关系JJJJJJJJJJJJJJJJJJJJJJJJ
如图,已知AB‖CD,角1=角B,角2=角D,判断BE与DE的位子关系
JJJJJJJJJJJJJJJJJJJJJJJJ

如图,已知AB‖CD,角1=角B,角2=角D,判断BE与DE的位子关系JJJJJJJJJJJJJJJJJJJJJJJJ
垂直

因为ab//cd
所以 角a+角c=180度
又因为 ( 角a+角b+角1)+(角c+角d+角2)=180度+180度
所以 角b+角1+角d+角2=180度
又因为 角1=角B,角2=角D
所以 角1+角2=90度
所以 角ced=90度
所以 BE//DE

∵AB‖CD
∴∠A+∠C=180º
∵∠1=∠B,∠2=∠D
∴∠A=180º-2∠1,∴∠C=180º-2∠2
∴180º-2∠1+180º-2∠2=180º
∴∠1+∠2=90º
∴∠BED=180º-(∠1+∠2)=90º
∴BE⊥DE