The document outlines geometric proofs, specifically two-column proofs that consist of statements and reasons. It includes examples of proofs involving supplementary angles, congruence, right angles, and various postulates and properties, along with a quiz section. Key components referenced include given information, definitions, postulates, theorems, and properties used in proving geometric statements.

1. Geometric Proofs27 October 2009

2. Geometric ProofsTWO COLUMN PROOFSFIVE KEY ELEMENTS GivenDiagramsProveStatementsReasons

3. ReasonsGiven InformationDefinitionsPostulatesPROPERTIESTheorems

4. Given: PROVE: STATEMENTS Reasons 1. 1. Given2. Definition of supplementary angles2. 3. Substitution Property3. 4. 4. Subtraction Property5. 5. Definition of Congruent Angles

5. Given: Prove: B123AC

6. Statements Reasons1.2.3.4.5.6.7.8.1.2.3.4.5.6.7.8.GivenDefinition of Right AngleAngle Addition PostulateSubstitution Property (Steps 2 and 3)GivenDefinition of Congruent AnglesSubstitution Property (Step 4 and 6)Definitions of Complementary Angles

7. Given: Prove: AX45˚BC

8. QUIZWhat is always the first step of a proof?Name 5 key elements of a proof.Name 5 types of reasons one can use during a proof.Measures __________: Angles and Segments are ______________.What is the last statement in a proof?

9. Statements Reasons1.2.3.4.5.6.7.8.9.1.2.3.4.5.6.7.8.9.GivenDefinitions of Angle BisectorDefinitions of Congruent AnglesGivenSubstitution PropertyAngle Addition PostulateSubstitution PropertySimplifyDefinition of Right Angle

10. Given: Prove: CDABE

11. Statements Reasons1.2.3.4.5.1.2.3.4.5.GivenGivenGivenDefinition of MidpointASA (Steps 1, 4, 2)

12. Given:Prove:1AD2BC

13. Statements ReasonsConverse of the Consecutive Interior Angles TheoremGivenPerpendicular Transversal TheoremGivenDefinition of Supplementary Angles

14. Given:Prove:BD1234AEC

15. Statements ReasonsSubstitution Property5.6.Given3.2.Corresponding Angles Postulate2.3.Given1.1.Substitution Property4.5.Converse of Corresponding Angles Postulate6.4.

16. Given:Prove:ZYXW

17. Statements Reasons1.2.3.4.5.1.2.3.4.5.Segment Addition PostulateSubstitution Property

18. Given:Prove:LM45ON

19. Statements Reasons1.2.3.4.5.6.1.2.3.4.5.6.Definition of Right AngleSubstitution Property