Alternate Exterior Angles Theorem
Pronunciation: /ˈɔl.tər.nɪt ɪkˈstɪər.i.ər ˈæŋ.gəlz ˈθɪər.əm/ Explain
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Figure 2: Transversal.
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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 Congruence Theorem
states that
vertical angles
are always 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 |
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References
- McAdams, David E.. All Math Words Dictionary, Alternate Exterior Angles Theorem. 2nd Classroom edition 20150108-4799968. pg 13. Life is a Story Problem LLC. January 8, 2015. Buy the book
Cite this article as:
McAdams, David E. Alternate Exterior Angles Theorem. 4/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/altexterioranglestheorem.html.
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Revision History
4/11/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
6/13/2018: Removed broken links, updated license, implemented new markup. (
McAdams, David E.)
5/5/2011: Initial version. (
McAdams, David E.)