Question

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

	statement	reason
1	$overline{uv} perp overline{vw}$	given
2	$overline{vw} perp overline{wx}$	given
3	$mangle uvw = 90^circ$
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: Justify right angle measure

Reason: Definition of perpendicular lines

Step2: Justify parallel lines from supplementary angles

Reason: Consecutive Interior Angles Converse

Answer:

1. For Statement 3, the missing reason is: Definition of perpendicular lines
2. For Statement 6, the missing reason is: Consecutive Interior Angles Converse