Question

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Use a paragraph proof to prove the same-side interior angles theorem.

Given: Line AB//CD

Prove: Same-side interior angles are supplementar

Answer 1

This is not a paragraph proof but you can easily change the format
to that of a paragraph proof.

Given: parallel lines AB and CD cut by transversal EF
Prove: <6 and <3 are supplementary; <4 and <5 are supplementary

1. Line AB // Line CD --> Given
2. <2 and <3 are supplementary --> If the exterior sides of two adjacent angles form opposite rays, then the angles are supplementary
3. m<2 + m<3 = 180 --> Definition of supplementary angles
4. <2 is congruent to < 6 --> If two parallel lines are cut by a transversal, corresponding angles are congruent (Postulate)
5. m<2 = m<6 --> Definition of congruent angles
6. m<6 + m<3 = 180 --> Substitution Property (In step 3, substitute m<6 for m<2)
7. < 6 and <3 are supplementary --> Definition of Supplementary Angles
8. By a similar argument, < 4 and < 5 are supplementary