Question

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

	statement	reason
2	$overline{vw} perp overline{wx}$	given
3	$mangle uvw = 90^circ$	definition of perpendicular lines
4	$mangle vwx = 90^circ$	definition of perpendicular lines
5	$mangle uvw + mangle vwx = 180^circ$	properties of addition, subtraction, multiplication, and division
6	$overline{wx} parallel overline{uv}$

Explanation:

Step1: Identify given perpendiculars

$\overline{UV} \perp \overline{VW}$, $\overline{VW} \perp \overline{WX}$ (Given)

Step2: Derive right angles

$m\angle UVW = 90^\circ$, $m\angle VWX = 90^\circ$ (Def. of perpendicular lines)

Step3: Sum the angle measures

$m\angle UVW + m\angle VWX = 90^\circ + 90^\circ = 180^\circ$ (Addition property)

Step4: Apply parallel line theorem

$\overline{WX} \parallel \overline{UV}$ (Consecutive interior angles converse)

Answer:

The missing reason for statement 6 is Consecutive Interior Angles Converse Theorem (if two lines are cut by a transversal and consecutive interior angles are supplementary, the lines are parallel)