Vertical Angle Theorum Proof

Vertical Angle Theorum: If two angles are vertical angles, then they have equal measures.

Given:

Statements/Conclusion	Justification
1) BEA and CED are vertical angles.	1) Given
2) and are opposite rays. and are opposite rays.	2) Definition of vertical angles
3) 1 and 3 are a linear pair. 2 and 3 are a linear pair.	3) Definition of linear pair
4) 1 and 3 are supplementary angles. 2 and 3 are supplementary angles.	4) Linear Pair Theorum
5) m1 + m3 = 180 degrees. m2 + m3 = 180 degrees.	5) Definition of supplementary angles
6) m1 + m3 = m2 + m3	6) Substitution Property
7) m3 = m3*	7) Reflexive Property
8) m1 = m2	8) Subtraction Property of Equality

* Step 7 is usually not necessary and is only included for clarification.

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- Jaime III
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