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

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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).

**Sources:**

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