Question

g.rlt2 angle pair relationships(non calculator) - sum
postulate / theorem / converse
what postulate, theorem, or converse justifies the statement about the diagram?
given: ( cparallel d ), how can you prove ( angle 2+angle 5 = 180^{circ} )
alternate interior angles converse
consecutive (same side) interior angles converse
alternate interior angles theorem
consecutive (same side) interior angles theorem

Explanation:

Step1: Recall the definitions

• Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
• Alternate Interior Angles Converse: If alternate interior angles are congruent, then the two lines are parallel.
• Consecutive (Same - side) Interior Angles Theorem: If two parallel lines are cut by a transversal, then consecutive (same - side) interior angles are supplementary ($\angle+\angle = 180^{\circ}$).
• Consecutive (Same - side) Interior Angles Converse: If consecutive (same - side) interior angles are supplementary, then the two lines are parallel.

Step2: Analyze the given angles

We are given that \(c\parallel d\) and we need to prove \(\angle2+\angle5 = 180^{\circ}\). Since \(c\) and \(d\) are parallel (given) and we are dealing with the sum of two angles (\(\angle2\) and \(\angle5\)) that are on the same side of the transversal and inside the two parallel lines.

Answer:

Consecutive (Same side) Interior Angles Theorem