Question

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

Given: Same-side interior angles are supplementary

prove: ab paralle to cd

Answer 1

A general method to follow is to always state what you're given and go from there

Given: Same-side interior angles are supplementary

Answer 2

So because we know that "Same-side interior angles are supplementary", we can say


m < 4 + m < 5 = 180


But we can also say that

m < 3 + m < 4 = 180

since angles 3 and 4 form a straight line

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So

m < 4 + m < 5 = m < 3 + m < 4

because the two are both equal to 180

Now subtract m < 4 from both sides to get

m < 5 = m < 3

or

m < 3 = m < 5


Now because those two angles are congruent, and those two angles are alternate interior angles, this means that line AB is parallel to line CD