1. Chapter 2.6
Algebraic Proof

2. Properties you need to know!

3. State the Property that justifies each statement
If 4 + (-5) = -1, Then x (-5) = x – 1
If 5 = y, Then y = 5
If 2a = -18, Then a= - 9

4. Prove that if 2x + 5 = 15, then x = 5
Statements
Reasons

5. Example 1 Statements Reasons
Justify Each Step When Solving an Equation
Prove that if 2(5 – 3a) – 4(a + 7) = 92, then a = -11
Statements
Reasons

6. Prove that if -3(a+3) + 5(3-a) = -50, then a = 7
Statements
Reasons

7. Postulates

8. Concept

9. Example 3
Write a Geometric Proof
If A B, mB = 2mC, and mC = 45, then mA = 90. Write a two-column proof to verify this conjecture.

10. Example 3 1. Given 1. A B; mB = 2mC; mC = 45 2. mA = mB
Write a Geometric Proof
Statements Reasons
Proof:
1. Given 1.
A B; mB = 2mC; mC = 45
2. mA = mB
2. Definition of angles
3. Transitive Property of Equality
3. mA = 2mC
4. Substitution 4.
mA = 2(45)
5. mA = 90
5. Substitution

11. Example 3

12. Example 3 1. Given 1. 2. 2. _______________ ? 3. AB = RS
Statements Reasons
Proof:
1. Given 1. 2.
2. _______________ ?
3. AB = RS
3. Definition of congruent segments
4. AB = 12
4. Given
5. RS = 12
5. Substitution

13. Write a two column proof for the conjecture.
If CD = EF, and CD=3y – 9, and EF = 15, then y = 8

14. Example 2 Begin by stating what is given and what you are to prove.
Write an Algebraic Proof
Begin by stating what is given and what you are to prove.

15. Try it!
Pg. 138 #3A
Pg. 139 #7