Question

Prove the Lines are Parallel detailed two column proof for the following Given: 1 and 3 are supplementary Prove: a || b​

Answer 1

The line a and b from the given line diagram is parallel since <2 and <3 are corresponding angles.

Column proof of angles

An angle is the point where two lines meet or intersect. From the given line diagram, we are told that <1 and <2 are supplementary.

Since the sum of supplementary angles is 180 degrees, hence;

<1 + <3 = 180 degrees

Also <1 + <2 = 180 degrees (sum of angles on a straight line)

<1 = 180 - <3

<1 = 180 - <2

Equate

180 - <3 = 180 - <2

-<3 = -<2

<2 = <3 (corresponding angle)

Since <2 is equivalent to <3, hence the line a is parallel to b

Learn more on line and angle theorem here: brainly.com/question/24839702

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