http://www.ck12.org Chapter 2. Reasoning and Proof
Example D
TheSame Angle Supplements Theoremstates that if two angles are supplementary to the same angle then the two
angles are congruent. Prove this theorem.
Given:^6 Aand^6 Bare supplementary angles.^6 Band^6 Care supplementary angles.
Prove:^6 A∼=^6 C
TABLE2.22:
Statement Reason1.^6 Aand^6 Bare supplementary
(^6) Band (^6) Care supplementary
- Given
2.m^6 A+m^6 B= 180 ◦
m^6 B+m^6 C= 180 ◦- Definition of supplementary angles
3.m^6 A+m^6 B=m^6 B+m^6 C 3. SubstitutionPoE
4.m^6 A=m^6 C 4. SubtractionPoE5.^6 A∼=^6 C 5.∼=angles have = measures
Example E
TheVertical Angles Theoremstates that vertical angles are congruent. Prove this theorem.
Given: Lineskandmintersect.
Prove:^61 ∼=^63
TABLE2.23:
Statement Reason- Lineskandmintersect 1. Given
2.^6 1 and^6 2 are a linear pair
(^6) 2 and (^6) 3 are a linear pair
- Definition of a Linear Pair
3.^6 1 and^6 2 are supplementary
(^6) 2 and (^6) 3 are supplementary
- Linear Pair Postulate
4.m^61 +m^62 = 180 ◦
m^62 +m^63 = 180 ◦- Definition of Supplementary Angles
5.m^61 +m^62 =m^62 +m^63 5. SubstitutionPoE
6.m^61 =m^63 6. SubtractionPoE7.^61 ∼=^63 7.∼=angles have = measures
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