来自姜月秋的问题
问:如图所示,AB‖CD,求证∠P=∠A+∠CA___________BP/C/___________D
问:如图所示,AB‖CD,求证∠P=∠A+∠C
A___________B
P
/
C/___________D
1回答
2020-01-29 10:37
问:如图所示,AB‖CD,求证∠P=∠A+∠CA___________BP/C/___________D
问:如图所示,AB‖CD,求证∠P=∠A+∠C
A___________B
P
/
C/___________D
证明:从P做PQ平行AB(Q在P左边)
∵PQ‖AB,AB‖CD.∴PQ‖CD(平行同一条直线的两直线平行)
AB‖PQ,∠A=∠APQ,(两直线平行,内错角相等)
CD‖PQ,∠C=∠CPQ(两直线平行,内错角相等)
∠P=∠APQ+∠CPQ=∠C+∠A(等量代换)