1. Geometry 9/5/14 - Bellwork

2. 2.6 Prove Statements about Segments and Angles
Objectives:
To understand the role of proof in a deductive system
To write proofs using geometric theorems

3. Premises in Geometric Arguments
The following is a list of premises that can be used in geometric proofs:
Definitions and undefined terms
Properties of algebra, equality, and congruence
Postulates of geometry
Previously accepted or proven geometric conjectures (theorems)

4. Amazing
Usually we have to prove a conditional statement. Think of this proof as a maze, where the hypothesis is the starting point and the conclusion is the ending. p q

5. Amazing
Your job in constructing the proof is to link p to q using definitions, properties, postulates, and previously proven theorems. p q

6. Example 1 Construct a two-column proof of:
If m1 = m3, then mDBC = mEBA.

7. Example 1
Given: m1 = m3 Prove: mDBC = mEBA
Statements
Reasons

8. Example 1 Given: m1 = m3 Prove: mDBC = mEBA Statements Reasons

9. Example 1 Given: m1 = m3 Prove: mDBC = mEBA Statements Reasons

10. Example 1 Given: m1 = m3 Prove: mDBC = mEBA Statements Reasons
2. m1 + m2 = m3 + m2

11. Example 1 Given: m1 = m3 Prove: mDBC = mEBA Statements Reasons
2. m1 + m2 = m3 + m2
2.Addition Property

12. Example 1 Given: m1 = m3 Prove: mDBC = mEBA Statements Reasons
2. m1 + m2 = m3 + m2
2.Addition Property
3. m1 + m2 = mDBC

13. Example 1 Given: m1 = m3 Prove: mDBC = mEBA Statements Reasons
2. m1 + m2 = m3 + m2
2.Addition Property
3. m1 + m2 = mDBC
3.Angle Addition Postulate

14. Example 1 Given: m1 = m3 Prove: mDBC = mEBA Statements Reasons
2. m1 + m2 = m3 + m2
2.Addition Property
3. m1 + m2 = mDBC
3.Angle Addition Postulate
4. m3 + m2 = mEBA

15. Example 1 Given: m1 = m3 Prove: mDBC = mEBA Statements Reasons
2. m1 + m2 = m3 + m2
2.Addition Property
3. m1 + m2 = mDBC
3.Angle Addition Postulate
4. m3 + m2 = mEBA
4.Angle Addition Postulate

16. Example 1 Given: m1 = m3 Prove: mDBC = mEBA Statements Reasons
2. m1 + m2 = m3 + m2
2.Addition Property
3. m1 + m2 = mDBC
3.Angle Addition Postulate
4. m3 + m2 = mEBA
4.Angle Addition Postulate
5. mDBC = mEBA

17. Example 1 Given: m1 = m3 Prove: mDBC = mEBA Statements Reasons
2. m1 + m2 = m3 + m2
2.Addition Property
3. m1 + m2 = mDBC
3.Angle Addition Postulate
4. m3 + m2 = mEBA
4.Angle Addition Postulate
5. mDBC = mEBA
5.Substitution Property

18. Two-Column Proof
Notice in a two-column proof, you first list what you are given (hypothesis) and what you are to prove (conclusion). The proof itself resembles a T-chart with numbered statements on the left and numbered reasons for those statements on the right. Before you begin your proof, it is wise to try to map out the maze from p to q.

19. Generic Two-Column Proof
Given: ____________ Prove: ____________
Insert illustration here
Statements
Reasons 1. 2. 3.

20. Theorems of Congruence
Congruence of Segments
Segment congruence is reflexive, symmetric, and transitive.

21. Theorems of Congruence
Congruence of Angles
Angle congruence is reflexive, symmetric, and transitive.

22. Assignment
Textbook PP : 3,4, 10-13, 16, 21, 22