Alternate Interior Angles Theorem
Pronunciation: /ˈɔl tər nɪt ɪnˈtɪər i ər ˈæŋ gəlz ˈθɪər əm/ Explain

Figure 2: Transversal.


Proof of the Alternate Interior Angles Theorem
Step  Description  Justification 
1  a  b  This is a criterion, a necessary condition. 
2  ∠1 ≅ ∠5  The Parallel Line Postulate states that, given a transversal of parallel lines, corresponding angles are congruent. 
3  ∠5 ≅ ∠7  The Vertical Angle Theorem states that vertical angles are congruent. 
4  ∠1 ≅ ∠7  The Transitivity of Congruence of Angles Theorem states that if two angles are congruent to the same angle, they are congruent to each other. In this case since ∠1 ≅ ∠5 and ∠5 ≅ ∠7, then ∠1 ≅ ∠7. 
5  ∠2 ≅ ∠8 Q.E.D.  A similar argument can be made to show that ∠2 ≅ ∠8. 
Table 1: Proof of the Alternate Interior Angles Theorem 

Cite this article as:
McAdams, David E. Alternate Interior Angles Theorem. 7/10/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/altinterioranglestheorem.html.
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Revision History
6/13/2018: Removed broken links, changed Geogebra links to work with Geogebra 5, updated license, implemented new markup. (
McAdams, David E.)
5/5/2011: Initial version. (
McAdams, David E.)