1. 2-6 Algebraic Proof p. 136
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.

2. Proofs
A proof is a logical argument in which each statement you make is supported by a statement that is accepted as true.
It can be written as:
A paragraph
Two column or formal
Flow chart.

3. Page 136

4. Algebraic Proofs
You just saw a table summarizing the properties of real numbers you studied in Algebra. Now you will use these properties in Algebraic Proofs. An algebraic proof is a proof that is made up of a series of algebraic statements.

5. 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 = 92 Distributive Property
–18 – 10a = 92 Substitution Property
–18 – 10a = Addition Property
–10a = 110 Substitution Property
Division Property
a = –11 Substitution Property
Answer: a = –11

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

7. Begin by stating what is given and what you are to prove.

8. *Hint* always start with GIVEN Always end with PROVE
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

9. 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

10. Statements Reasons
Proof: 3.
3. Division Property of Equality 4.
4. Symmetric Property of Equality
1. Given 1.
2. _____________
2. Multiplication Property of Equality ?
2A = (b1 + b2)h

11. 3. Transitive Property of Equality 3. mA = 2mC
If A B, mB = 2mC, and mC = 45, then mA = 90. Write a two-column proof to verify this conjecture.
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

12. 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
Transitive Property of Equality

13. 2-6 Assignment
Page 139, 2-16 even, 17, 18 Write out all of the information in the book for 17 & 18 That includes: Given Prove Statements Reasons