1. 5.2 Notes: Algebraic Proof
Date:
5.2 Notes: Algebraic Proof
Lesson Objective: Use algebra to write 2-column proofs and use the properties of equa-lity to write geometric proofs.
CCSS: G.CO.9 Prove theorems about lines and angles.
This is Jeopardy!!!: This is the value of x in 3x – 4 = 4.
Staple the following table into your notes.

4. Lesson 1: The Properties Game
Name the property used to get the bottom equation.
Hide your answer until time is called.
No last-second answer changes will be allowed.
Total points will be divided evenly among the number of teams with the correct answer.

5. Lesson 1: The Properties Game
Show your work: write the equations as shown with the property numbered with the same number to the right.
Do not duplicate the equations.

6. Lesson 1: The Properties Game
1. -5(x + 4) = Given
2. (-5)x + (-5)4 = 70 2.
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

7. Lesson 1: The Properties Game
1. -5(x + 4) = Given
2. (-5)x + (-5)4 = Dist. Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

8. 2. (-5)x + (-5)4 = Dist. Prop. =
3. -5x – 20 =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

9. 2. (-5)x + (-5)4 = Dist. Prop. =
3. -5x – 20 = Substitution
Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

10. 3. -5x – 20 = Substitution
Prop. =
4. -5x – =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

11. 3. -5x – 20 = Substitution
Prop.
4. -5x – = Addition Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

12. 4. -5x – = Addition Prop. =
5. -5x =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

13. 4. -5x – = Addition Prop. =
5. -5x = Substitution Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

14. 5. -5x = 90 5. Substitution Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

15. 5. -5x = 90 5. Substitution Prop. =
6. -5x = Division Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

16. 6. -5x = Division Prop. =
7. x =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

17. 6. -5x = Division Prop. =
7. x = Substitution Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

18. Properties Game Continued
State the property that justifies the statement.
A. If x = 5, then x = 20 4
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

19. Properties Game Continued
State the property that justifies the statement.
A. If x = 5, then x = 20 A. Multiplication
Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

20. State the property that justifies the statement.
B. XY = XY
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

21. State the property that justifies the statement.
B. XY = XY B. Reflexive Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

22. State the property that justifies the statement.
C. If 2x + 5 = 11, then 2x = 6
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

23. State the property that justifies the statement.
C. If 2x + 5 = 11, then 2x = 6
C. Subtraction Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

24. State the property that justifies the statement.
D. If m/ 1 = m/ 2 and m/ 2 = m/ 3,
then m/ 1 = m/ 3.
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

25. State the property that justifies the statement.
D. If m/ 1 = m/ 2 and m/ 2 = m/ 3,
then m/ 1 = m/ 3.
D. Transitive Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

26. State the property that justifies the statement.
E. If 5 = y, then y = 5
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

27. State the property that justifies the statement.
E. If 5 = y, then y = 5 E. Symmetric
Prop. =
Teams:
1. ______ 2. ______ 3. ______ 4. ______
5. ______ 6. ______ 7. ______ 8. ______

28. Lesson 2: Write an Algebraic Proof for a Real-World Example with Mrs
Lesson 2: Write an Algebraic Proof for a Real-World Example with Mrs. Dawson
SCIENCE If the formula to convert a Rankine tempera-ture to a Celsius temperature is C = 5/9(R – ), then the formula to convert a Celsius temperature to a Rankine temperature is R = 9/5C Write a two-column proof to verify this conjecture.

29. Lesson 2: Write an Algebraic Proof for a Real-World Example with Mrs
Lesson 2: Write an Algebraic Proof for a Real-World Example with Mrs. Dawson
SCIENCE If the formula to convert a Rankine tempera-ture to a Celsius temperature is C = 5/9(R – ), then the formula to convert a Celsius temperature to a Rankine temperature is R = 9/5C Write a two-column proof to verify this conjecture.
Given: C = 5/9(R – )
Prove: R = 9/5C

30. Lesson 3: Write a Geometric Proof with Mr. R
On a clock, the angle formed by the hands at 4:00 is a 120°. If the angle formed at 4:00 is congruent to the angle formed at 8:00, prove that the angle formed at 8:00 is a 120° angle.

31. Lesson 3: Write a Geometric Proof with Mr. R
On a clock, the angle formed by the hands at 4:00 is a 120°. If the angle formed at 4:00 is congruent to the angle formed at 8:00, prove that the angle formed at 8:00 is a 120° angle.
Given: m/ 4 = 120°
Prove: m/ 8 = 120°  

32. 5.2 Algebraic Proofs: Do I Get It? Yes or No