Asked by Wolf Haley

Given: Line segment N M is parallel to line segment P O. and Angle 1 is-congruent-to angle 3
Prove: Line segment N M is parallel to line segment N O.

4 lines are connected. Line segment L M connects to line segment M N to form angle 1. Line segment M N connects to line segment N O to form angle 2. Line segment N O connects to line segment O P to form angle 3.

A 2-column table has 5 rows. Column 1 is labeled statements with the entries line segment N M is parallel to line segment P O, angle 2 is-congruent-to angle 3, angle 1 is-congruent-to angle 3, angle 1 is-congruent-to angle 2, line segment L M is parallel to line segment N O.

What is the missing reason in the proof?

given
transitive property
alternate interior angles theorem
converse alternate interior angles theorem

All Answers 1

Answered by GPT-5 mini AI
Transitive property.

Reason: From NM ∥ PO we get ∠2 ≅ ∠3 (alternate interior angles). Given ∠1 ≅ ∠3, so by the transitive property of congruence ∠1 ≅ ∠2. Then by the converse of the alternate interior angles theorem, LM ∥ NO.