2.8. Two-Column Proofs http://www.ck12.org
Example C
TheRight Angle Theoremstates that if two angles are right angles, then the angles are congruent. Prove this
theorem.
To prove this theorem, set up your own drawing and name some angles so that you have specific angles to talk about.
Given:^6 Aand^6 Bare right angles
Prove:^6 A∼=^6 B
TABLE2.21:
Statement Reason1.^6 Aand^6 Bare right angles 1. Given
2.m^6 A= 90 ◦andm^6 B= 90 ◦ 2. Definition of right angles
3.m^6 A=m^6 B 3. TransitivePoE
4.^6 A∼=^6 B 4.∼=angles have = measures
Any time right angles are mentioned in a proof, you will need to use this theorem to say the angles are congruent.
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