Question

ving same side interior angles supplementary
given: ( w parallel x ) and ( y ) is a transversal.
prove: ( angle 3 ) and ( angle 5 ) are supplementary.
use the drop - down menus to complete the proof.
given that ( w parallel x ) and ( y ) is a transversal, we know that ( angle 1congangle 5 ) by the
. therefore, ( mangle 1 = mangle 5 ) by the
definition of congruent. we also know that, by definition, ( angle 3 ) and ( angle 1 ) are alinear pair so they are supplementary by the
. by the
, ( mangle 3+mangle 1 = 180 ). now we can
substitute ( mangle 5 ) for ( mangle 1 ) to get ( mangle 3+mangle 5 = 180 ). therefore, by the
definition of supplementary angles, ( angle 3 ) and ( angle 5 ) are supplementary.

Explanation:

• First blank: When two parallel lines (\(w\parallel x\)) are cut by a transversal (\(y\)), \(\angle1\) and \(\angle5\) are in the position of corresponding angles. Corresponding angles postulate states that if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
• Second blank: \(\angle3\) and \(\angle1\) form a linear pair. The linear - pair postulate states that if two angles form a linear pair, then they are supplementary.
• Third blank: Since \(m\angle3 + m\angle1=180^{\circ}\) (from the linear - pair postulate) and \(m\angle1 = m\angle5\) (from the corresponding angles postulate), we use the substitution property of equality (if \(a = b\), then \(a\) can be substituted for \(b\) in any equation).

Answer:

1. Corresponding Angles Postulate
2. Linear - Pair Postulate
3. Substitution Property of Equality