Step-by-step explanation: this theorem is in fact true. perpendicular lines mean one line cuts through another line and forms 90 degree angles. if two lines were to cut through the same line, then both lines would have to be parallel to each other considering the definition of perpendicular lines. for example in the picture both lines are completely horizontal making them form 90 degree angles. if these lines did not form 90 degree angles then they would not be perpendicular and at some point would cross paths. however they are straight meaning they will never touch, hence the parallel line definition.
1)1st Statement: Reason: Given 2) 2nd Statement: Reason: Lines are perpendicular when form right angles by meeting another line. 3) 3rd Statement: Reason: Definition of Right Angles. 4) 4th Statement: Reason: Congruent angles have the same angle measure. 5) 5th Statement: Reason: If their corresponding angles are congruent, then their lines are parallel. (Corresponding Angles Theorem).
