Chapter 3.2, Problem 13WE

To determine

To prove: $t\perp n$ for the given parallel lines $l$ and $n$ such that $t\perp l$ ; $l\parallel n$ .

Explanation of Solution

Given information:

Given figure,

Given table for proof,

Statements	Reasons
$t\perp l$
$m\angle 1=90$
	Given
$\angle 2\cong \angle 1\text{or}m\angle 2=m\angle 1$
	Substitution Property
$t\perp n$

Calculation:

Refer to the figure provided in the text book.

Traversal $t$ cuts $l$ and $n$ ;

  $t\perp l$ ; $l\parallel n$ .

Proof is as follows:

Statements	Reasons
$t\perp l$	Given
$m\angle 1=90$	Definition of perpendicular of line
	Given
$\angle 2\cong \angle 1\text{or}m\angle 2=m\angle 1$	If two parallel line are cut by a traversal than corresponding angles are congruent or equal
$m\angle 2=90°$	Substitution Property
$t\perp n$	Definition or perpendicular of line.