Lesson 14 3 Proving Lines Parallel The converse

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Lesson 14. 3: Proving Lines Parallel The converse of a conditional statement, “if p,

Lesson 14. 3: Proving Lines Parallel The converse of a conditional statement, “if p, then q”, is the statement, “if q, then p”. That is, to write the converse of a conditional statement, just interchange the hypothesis and conclusion. Note: The converse of a conditional statement is not necessarily true.

Your Turn Complete the Explore section, parts A through D and Reflect 1 and

Your Turn Complete the Explore section, parts A through D and Reflect 1 and 2.

Postulate Converse of Same-Side Interior Angles Postulate If two lines are cut by a

Postulate Converse of Same-Side Interior Angles Postulate If two lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the lines are parallel.

Theorems Convers of Alternate Interior Angles Theorem If two lines are cut by a

Theorems Convers of Alternate Interior Angles Theorem If two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel. Converse of Alternate Exterior Angles Theorem If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.

One More Theorem Convers of Corresponding Angles Theorem If two lines are cut by

One More Theorem Convers of Corresponding Angles Theorem If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.

Prove the Converse of the Corresponding Angles Theorem Given: Prove:

Prove the Converse of the Corresponding Angles Theorem Given: Prove:

The Parallel Postulate Given a line and a point not on the line, exactly

The Parallel Postulate Given a line and a point not on the line, exactly on line can be drawn through the point so that it is parallel to the given line. If , then