1. 1. SWBAT use algebra to write two column proofs
Objectives:
1. SWBAT use algebra to write two column proofs
2. SWBAT use properties of equality to write geometric proofs
Splash Screen

2. Preparation for G.CO.9 Prove theorems about lines and angles.
Content Standards
Preparation for G.CO.9 Prove theorems about lines and angles.
Mathematical Practices
3 Construct viable arguments and critique the reasoning of others.
CCSS

3. Use algebra to write two-column proofs.
You used postulates about points, lines, and planes to write paragraph proofs.
Use algebra to write two-column proofs.
Use properties of equality to write geometric proofs.
Then/Now

4. algebraic proof
two-column proof
formal proof
Vocabulary

5. Properties of Real Numbers: properties are true for any real numbers a, b, and c

6. Justify Each Step When Solving an Equation
Solve 2(5 – 3a) – 4(a + 7) = 92.
Algebraic Steps Properties
2(5 – 3a) – 4(a + 7) = 92 Original equation
10 – 6a – 4a – 28 = Distributive Property
–18 – 10a = Substitution Property
–18 – 10a = Addition Property
–10a = Substitution Property
Division Property
a = – Substitution Property
Example 1

7. Solve –3(a + 3) + 5(3 – a) = –50. A. a = 12 B. a = –37 C. a = –7
D. a = 7
Example 1

8. 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.
Example 2

9. 2. Addition Property of Equality
Write an Algebraic Proof
Statements Reasons
Proof:
1. Given 1.
d = 20t + 5
2. d – 5 = 20t
2. Addition Property of Equality 3.
3. Division Property of Equality
= t 4.
4. Symmetric Property of Equality
Example 2

10. Which of the following statements would complete the proof of this conjecture?
If the formula for the area of a trapezoid is , then the height h of the trapezoid is given by
Example 2

11. 3. Division Property of Equality
Statements Reasons
Proof: 3.
3. Division Property of Equality 4.
4. Symmetric Property of Equality
1. Given 1.
2. _____________
2. Multiplication Property of Equality ?
Example 2

12. A. 2A = (b1 + b2)h B. C. D.
Example 2

13. Write a Geometric Proof
Example 3

14. Proof: Statements Reasons 1. Given 2. Definition of ≅ angles
3. Transitive Property of Equity
4. Substitution
5. Substitution

15. Example 3

16. 3. Definition of congruent segments
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
Example 3

17. A. Reflexive Property of Equality B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality
Example 3

18. HOMEWORK
Page 139 #’s 9-20