Proofs Parallel Lines

If ∠1 ≅ ∠3, then ________.

• line c is parallel to line d

• line a is parallel to line b

• Cannot determine 2 lines to be parallel.

• line c is parallel to line a

• line b is parallel to line d

If ∠9 ≅ ∠12, then ________.

• line a is parallel to line b

• line d is parallel to line c

• none of the lines can be determined to be parallel.

• line a is parallel to line d

• line c is parallel to line b

If ∠11 ≅ ∠7, then ________.

• line b is parallel to line a

• line c is parallel to line a

• line b is parallel to line d

• line c is parallel to line d

• Cannot determine 2 lines to be parallel.

1) Which statement restates the Given from the question?

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2) Which statement represents what you have to prove from the question?

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What is the reason for Statement 4 to complete the proof?

• Converse of Corresponding Angles Postulate

• Transitive Property of Congruence

• Substitution

• Algebra

What is the reason for Statement 4?

• Substitution

• Converse of Alternate Exterior Angles Theorem

• Converse of Corresponding Angles Postulate

• Converse of Same-side Interior Angles Theorem

Supply the second reason.

• Linear Pair Postulate

• Alternate Interior Angles Theorem

• Vertical Angles Theorem

• Corresponding Angles Postulate

The last statement is <4 = <6. What is the last reason

• Prove

• Definition of congruent angles

• Transitive Property

• Alternate Interior Angles Theorem

Which is the correct reason for statements 2 and 4 in the proof?

• Corresponding Angles

• Substitution

• Definition of Congruent Angles

• Vertical Angles are congruent.