Answer: The reason of 2nd statement is "Converse of corresponding angle post". The reason of 3rd statement is "given". The reason for 4th statement is "perpendicular transversal theorem".
Explanation:
It is given that in the figure angle 1 and 2 are congruent angles. It is also given that the line p is perpendicular to r.
We have to prove line q is perpendicular to r.
it is given that angle 1 and 2 are congruent angles, since line p is perpendicular to line r it means angle 1 and 2 are 90 degree.
Since angle 2 and 3 are supplementary angles it means their sum is 180 degree. Angle 2 is 90 it means angle 3 is also 90 degree.
Since the corresponding angle are same, it means the lines are parallel.
It is given that the line p is perpendicular to r.
The perpendicular transversal theorem states that if two lines are perpendicular to the same line then the lines are parallel to each other.
Since the lines are parallel and bth are perpendicular to the same line, therefore, by perpendicular transversal theorem the line q is perpendicular to line r.
