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歡迎您訪問數(shù)學(xué)考題練習(xí):已知三條不同的直線a、b、c在同一平面內(nèi),下列!

數(shù)學(xué)考題練習(xí):已知三條不同的直線a、b、c在同一平面內(nèi),下列

更新時(shí)間:2024-01-12 14:02:28作者:貝語網(wǎng)校

已知三條不同的直線a、b、c在同一平面內(nèi),下列四條命題:①如果a//b,a⊥c ,那么b⊥c; ②如果b//a,c//a,那么b//c;③如果b⊥a,c⊥a ,那么b⊥c;④如果b⊥a,c⊥a ,那么b//c.其中真命題的是________.(填寫所有真命題的序號(hào))

試題答案

根據(jù)平行公理的推論“如果兩條直線都和第三條直線平行,那么這兩條直線平行”和“垂直于同一條直線的兩直線平行”進(jìn)行分析判斷.

①如果a∥b,a⊥c,那么b⊥c是真命題,故本選項(xiàng)正確,

②如果b∥a,c∥a,那么b∥c是真命題,故本選項(xiàng)正確,

③如果b⊥a,c⊥a,那么b⊥c是假命題,故本選項(xiàng)錯(cuò)誤,

④如果b⊥a,c⊥a,那么b∥c是真命題,故本選項(xiàng)正確,

故答案為①②④.
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