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.
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.
Page 136
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.
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
10 – 6a – 4a – 28 = 92
Original equation
Distributive Property
–18 – 10a = 92
Substitution Property
–18 – 10a + 18 = 92 + 18
–10a = 110
Addition Property
Substitution Property
Division Property
a = –11
Answer: a = –11
Substitution Property
Solve –3(a + 3) + 5(3 – a) = –50.
A. a = 12
B. a = –37
C. a = –7
D. a = 7
Begin by stating what is given and what you are to
prove.
*Hint* always start with GIVEN
Always end with PROVE
Proof:
Statements
Reasons
1. d = 20t + 5
1. Given
2. d – 5 = 20t
2. Addition Property of Equality
3.
4.
=t
3. Division Property of Equality
4. Symmetric Property of
Equality
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
.
Proof:
Statements
Reasons
1.
1. Given
2. _____________
2A = (b?1 + b2)h
2. Multiplication Property of
Equality
3.
3. Division Property of Equality
4.
4. Symmetric Property of
Equality
If A B, mB = 2mC, and mC = 45, then
mA = 90. Write a two-column proof to verify this
conjecture.
Proof:
Statements
Reasons
1. A B;
mB = 2mC;
mC = 45
1. Given
2. mA = mB
2. Definition of
3. mA = 2mC
3. Transitive Property of
Equality
4. mA = 2(45)
4. Substitution
5. mA = 90
5. Substitution
angles
Proof:
Statements
1.
2.
Reasons
1. Given
? Property of Equality
2. _______________
Transitive
3. AB = RS
3. Definition of congruent
segments
4. AB = 12
4. Given
5. RS = 12
5. Substitution
2-6 Assignment
Page 139, 10 -16 even, 17, 18
Write out all of the information in the book for
17 & 18
That includes:
Given
Prove
Statements
Reasons