Question

同一平面内的四条直线满足a垂直于b，b垂直于c，c垂直于d，则下列句子成立的是（） A.a平行b B.b垂直d C.a

同一平面内的四条直线满足a垂直于b，b垂直于c，c垂直于d，则下列句子成立的是（） A.a平行b B.b垂直d C.a垂直d D.b平行c

Answer 1

A不对，a垂直于b，则在同一平面内a部可能平行于b，D不对，同理可证。
B不对，在同一平面内，直线b垂直于直线c，直线d垂直于直线c，则推出直线b平行于直线d，所以见A可知不对。
C正确。排除法出来了，不过也可以证明。
在同一平面内，直线a垂直于直线b，直线c垂直于直线b，推出直线a平行于直线c。
又因为直线d垂直于直线c，所以直线a垂直于直线d。
建议做图，可以把一张纸看成一个平面，注意条件同一平面内，毕竟如果不是同一平面内，则四个答案全错。

Answer 2

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Answer 3

C.a垂直于d

Answer 4

C a垂直b

Answer 5

C.a垂直d

追问

Why?

追答

∵a⊥b,c⊥b
∴a∥c 。 ﹙平面内垂直于同一条直线的两条直线平行﹚
∵c⊥d
∴a⊥d。﹙平面内如果两条直线平行中有一条垂直于已知直线，那么另一条也垂直于已知直线﹚