Proving Lines Are Parallel

Question

Given: p ll q; <1 and <4 are supplementary

Prove: r ll s

The picture is in here and have to use all lines:

https://drive.google.com/drive/folders/13ODk_8fNotUI44tiH5IaXliy8KgYt6OG?usp=sharing

Answer 1

given 1 and 4 are supplmentary

p || q

Prove r || s

angle 1 and angle2 are supplementary : Theorem stating that 2 adjacent angles whose

exterior rays form a line are supplementary

angle 1 + angle 2 = 180 : definition of supplementary

angle 1 + angle 4 = 180 : definition of supplementary

angle 1 + angle2 = angle1 + angle 4 : substitution/transitive

angle 2 = angle 4 : subtraction property of equality

angle 4 = angle 5: vertical angles are congruent

angle 5 = angle 8 : parallel lines, alternate angles

are congruent (same side of the railroad tracks)

angle 2 = angle 4 = angle 5 = angle 8 : substitution/transitive

R||s : converse of parallel lines/alternate angles are congruent;

angle2 and angle 8 are on the same side of the

railroad tracks with respect to lines r and s;

therefore they must be parallell