10 points Use the AIA Theorem to prove its corollary it is b

(10 points) Use the AIA Theorem to prove its corollary (it is basically just a line).

AIA Theorem: If two lines cut by a transversal have a pair of congruent alternate interior angles with respect to the transversal, then the two lines are parallel.

Corollary: Two lines perpendicular to the same line are parallel.

Solution

let say m and n are two lines both perpendicular to the line l, then

l is the transversal to m and n. the alternate interior angles are right angles.

all right angles are congurent, so the alternate interior angle theorem applies. so m and n are parallel.