Question

用反证法证明：在同一平面内，如果两条直线都和第三条直线垂直，那么这两条直线平行

过程要详细

Answer 1

假设两条直线都和第三条直线垂直，这两条直线不平行。

因为 两直线和第三条直线垂直
两条直线不平行
所以 这上边可以构成一个三角形
因为 两直线和第三条直线垂直
所以 有2个角是90度的
所以 三角形三个角加起来大于180度
所以 两直线不可能不平行
所以 在同一平面内，如果两条直线都和第三条直线垂直，那么这两条直线平行

Answer 2

假设这两条直线不平行 ，则这两条直线相交
那么过这个交点向第三条直线作垂线可以作两条，这与过直线外一点向已知直线作垂线有且只能作一条向矛盾 ；故假设不成立
所以：在同一平面内，如果两条直线都和第三条直线垂直，那么这两条直线平行

Answer 3

因为 两直线和第三条直线垂直
两条直线不平行
所以 这上边可以构成一个三角形
因为 两直线和第三条直线垂直
所以 有2个角是90度的
所以 三角形三个角加起来大于180度
所以 两直线不可能不平行
所以 在同一平面内，如果两条直线都和第三条直线垂直，那么这两条直线平行

Answer 4

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