Question

Complete the two-column proof.

Given: ∠2 and ∠5 are supplementary
Prove: l is parallel to m



Statements Reasons
1. _____________ 1. __________
2. ∠ 3 ∠ 2 2. __________
3. ∠ 3 and ∠ 5 are supplementary 3. _________
4. _____________ 4. _____________
Ill attach the picture.

Answer 1

Ill give a medal and fan!

Answer 2

angle 2 equals angle 3 (vertically opposite angles)
so angle 3 and angle 5 are supplementary
so l is parallel to m ( as interior angles on same side of transversal are supplementary)

Answer 3

Statements
<2 and <5 are supplementary
<2 <3
<3 and <5 are supplementary
<2 + <5 =180°
<3 + <5 =180°
line l || line m
Reasons
Given
Vertical Angle Theorem
Converse of Same-Side Interior Angles Theorem
Definition of Supplementary Angles
Definition of Supplementary Angles
Substitution

Answer 4

Thank you so much!

Answer 5

No problem!