Geometry worksheet focusing on the Converse of the Same Side Interior Angles Theorem with diagrams and proof exercises.

1. Given: ∠1 and ∠2 are supplementary
Prove: l || m

Statements:
1. ∠1 and ∠2 are supplementary
2. ∠2 and ∠3 are supplementary
3. ∠1 ≅ ∠3
4. l || m

Reasons:
1. Given
2. Linear Pair Theorem
3. Congruent Supplements Theorem
4. Converse of the Corresponding Angles Postulate

2. Given: a || b, c || d
Prove: ∠1 ≅ ∠3

Statements:
1. a || b, c || d
2. ∠1 ≅ ∠2
3. ∠2 ≅ ∠3
4. ∠1 ≅ ∠3

Reasons:
1. Given
2. Alternate Interior Angles Theorem
3. Corresponding Angles Postulate
4. Transitive Property of Congruence

3. Given: a || b, c || d
Prove: ∠1 + ∠4 = 180°

Statements:
1. a || b, c || d
2. ∠1 ≅ ∠2
3. ∠2 + ∠4 = 180°
4. ∠1 + ∠4 = 180°

Reasons:
1. Given
2. Definition of Supplementary Angles
3. Corresponding Angles Postulate
4. Substitution Property of Equality