Line a intersects lines c and d, creating a right angle on line c. Line b intersects lines c and d, creating a right angle on line d.
Write the following proof.
Prove: c ll d
Statements: Reasons: (State Theorems and postulates)
a ll b, a`_|_` c, and b`_|_`d 1.Given
Here is the image.
Given that line a is parallel to line b.
Line c intersects line a at right angle.
Therefore, according to the theorem “If a line is perpendicular to one of two given parallel lines, then it is also perpendicular to the other line”, line c must intersect line b too at right angle.
Now considering line b intersecting the two lines c and d, it is given that it intersects line d at right angle. Then, the abovementioned theorem proves that it intersects line c at right angle.
So, lines c and d are two lines, cut by a transversal (line b), and the corresponding angles are equal to 90°, hence congruent.
Therefore, according to the transversal theorem “If two lines are cut by a transversal, so that corresponding angles are congruent, then the lines are parallel”, these two lines are parallel.
`rArr` c ll d (proved).