3-4+Proving+Lines+are+Parallel

3-4 Proving Lines are Parallel

==To use the theorems that you have learned in section 3.3, you must first know that two lines are parallel. Provided in this section, use the following postulates and theorems to prove that two lines are parallel. This section will teach you how to prove that lines are parallel. Also, this section shows you how to use the properties of parallel lines to solve real-life problems, such as proving that the mounds in Egypt are parallel. The following theorems are the converses of the ones you have learned in section 3.3. REMEMBER - that the converse of a true conditional statement is not necessarily true. However, each of the following converses MUST be proven to be true.==


 * Here are some sample problems**





Postulate 16: Corresponding Angles Converse

The lines are parallel if the two corresponding angles are congruent when it is cut by a transversal.

[[image:Screen_shot_2012-01-18_at_3.58.52_PM.png]]
If the measurement of angle m<4 + m<5= 180, then j || k

Theorem 3.10: Alternate Exterior Angles Converse The lines are parallel if the alternate exterior angles are congruent and are cut by a transversal.



If <5 ≅ <6, then j || k

PRACTICE REVIEW

Solution: Given à <1≅ <2

Prove: m||n




 * || Given ||
 * || Vertical Angles Theorem ||
 * || Transitive Property of Congruence ||
 * || Corresponding Angles Converse ||

Find the value of X that makes j||k



Given: <1 + <3= 180 Solution: l||m


 * <  || Given ||
 * <  || Definition of linear pair ||
 * <  || Corresponding Angles Theorem ||
 * <  || Transitive Property ||
 * <  || Vertical angles Theorem ||
 * <  || Transitive Property ||
 * <  || Converse of Corresponding Angles ||

Given: < 7 + <8= 180 Solution: A || B




 * <  || Given ||
 * <  || Linear Pair Postulate ||
 * <  || Alternate Exterior theorem ||
 * <  || Converse of Alternate Exterior Theorem ||

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