Question

$overline{xy} perp overline{wx}$ and $overline{vw} perp overline{wx}$. complete the proof that $overline{xy} parallel overline{vw}$.

	statement	reason
2	$overline{vw} perp overline{wx}$	given
3	$mangle vwx = 90^circ$	definition of perpendicular lines
4	$mangle wxy = 90^circ$
5	$mangle vwx + mangle wxy = 180^circ$	properties of addition, subtraction, multiplication, and division
6	$overline{xy} parallel overline{vw}$	converse of same - side interior angles theorem

Explanation:

Step1: Recall the definition of perpendicular lines

Perpendicular lines form a 90° angle. Since \(\overline{XY} \perp \overline{WX}\) (given in step 1), by the definition of perpendicular lines, the angle between them (\(\angle WXY\)) should be 90°.

Step2: Apply the definition to \(\overline{XY} \perp \overline{WX}\)

The reason for \(m\angle WXY = 90^\circ\) is the same as the reason for \(m\angle VWX = 90^\circ\), which is the definition of perpendicular lines.

Answer:

Definition of perpendicular lines