2.6 Geometric Proof
Theorem—a conjecture that can be proved to be true. Once you have proven a theorem, you
can use it as a reason in later proofs.
Proof—A convincing argument that can be used to show a conjecture is true.
When we write a proof, we give statements and then the reasons for each statement.
Hypothesis:--the information we are given
Conclusion—the statement we are trying to prove.
hypothesis
Definitions
Postulates
Properties
Theorems
Conclusion
2-6-1 Linear Pair Theorem—If two angles from a linear pair, then they are supplementary.
< ADC and < CDB are a linear pair, then m<ADC + m<CDB = 180°
2-6-2 Congruent Supplements Theorem—If two angles are supplementary to the same angle,
(or to two congruent angles), then the two angles are congruent.
If < ABC and < GHI are supplementary and < DEF and < GHI are supplementary, then
< ABC  < DEF.
2-6-3 Right Angle Congruence Statement—All right angles are congruent
2-6-4 Congruent Complements Theorem-- If two angles are complementary to the same
angle (or two congruent angles, then the two angles are congruent
If < ABC and < GHI are complementary and < DEF and < GHI are complementary, then
<ABC  < DEF.
2-7-1 Common Segment Theorem—Given collinear points A, B, C, D arranged as shown, if
AB  CD, then AC  BD

2-7-2 Vertical Angles Theorem-Vertical angles are congruent
<1 and < 3 are vertical angles
< 2 and < 4 are vertical angles
<1  < 3, < 2  < 4
2-7-2 If two congruent angles are supplementary, then each angle is a right angles
(  <’s sup
rt <’s)
If < 1 and < 2 are congruent and < 1 and < 2 are supplementary, then <1 and < 2 are right
angles.)