Chapter 2.6, Problem 8ST2

To determine

To prove: If $j\perp k$ in the given figure.

Answer to Problem 8ST2

Using below two column proof, it can be planned that lines j and k are perpendicular or $j\perp k$ .

Explanation of Solution

Given information: In given figure, $\angle 1$ is supplementary to $\angle 3$ and $\angle 2$ is supplementary to $\angle 3$ .

  

Concept used: Use following two properties:

1. Transitive property
2. Linear pair, so that the opposite rays of two adjacent angles form a straight angle of 180 degree.

Use following two column proof,

Statement	Reason
$\angle 1$ is supplementary to $\angle 3$	Given
$\angle 2$ is supplementary to $\angle 3$	Given
$\angle 2+\angle 3=180$	Definition of supplementary angles
$\angle 1+\angle 3=180$	Definition of supplementary angles
$\angle 1=\angle 2$	Subtraction property of equality
$\angle 1+\angle 2=180$	Linear pair
$2\angle 1=180$	Just proved
$\angle 1=90$	Division property of equality
$j\perp k$	Definition of perpendicular lines.