State whether the following is true or false: Two lines perpendicular to the same line will intersect each other.
Let’s consider the line 𝐴𝐵. If we draw two lines that are perpendicular to 𝐴𝐵, where perpendicular lines meet 𝐴𝐵 at 90 degrees, we can see that these two new lines are parallel. This is because they have the same slope or gradient.
As the two lines are parallel, the statement “two lines perpendicular to the same line will intersect each other” is false as parallel lines will never intersect each other.