Question

Proofs 50 points for whole page ( serious answers only or report and 1 star )

Answer 1

Question 1:

1) Given - This is given in the question.

2) Reflexive Property of Equality - Anything is equal to itself

3) Substitution Property of Equality - Due to the given, substituting 118° for m∠1 and 62° for m∠2 will not change the equality of the equation

4) Simplify - No need to explain as they have already given this

5) Definition of Supplementary Angles - Two angles are supplementary only when the sum of their measures is 180°.

6) Converse of Same-side Interior Angles Theorem - If there is a transversal intersecting two lines and the same-side interior angles formed are supplementary, then the lines are parallel.

Question 2:

1) Given - It is given in the question

2) Vertical Angles Theorem - Vertical angles have the same measure, making their angles congruent

3) Transitive Property of Congruence - Since it's given that
`\angle1\cong\angle3` and in step 2 we showed that
`\angle3\cong\angle4`, we can say that
`\angle1\cong\angle4`

4) Transitive Property of Congruence - Since we proved that
`\angle1\cong\angle4` and it's given that
`\angle4\cong\angle5`, we can say that
`\angle1\cong\angle5`

5) Converse of Alternate Interior Angles Theorem - If a transversal intersects two lines and the measures of alternate interior angles formed are equal, then the lines are parallel.