Perpendicular Transversal Theorem

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line also.

 

Given:

kl,tk

Prove:

tl

Proof

Statement
Reason
1
kl,tk
Given
2
1 is a right angle
Definition of perpendicular  lines
3
m1=90°
Definition of right angle
4
12
Corresponding angles
5
m1=m2
Definition of congruent angles
6
m2=90°
Substitution Property
7
2 is a right angle
Definition of right angle
8
tl
Definition of perpendicular lines