• algebraic proof – Made up of algebraic statements
• two-column proof/formal proof – contains statements and reasons in two columns
STEP
1. 3x = 7 – 1/2x
2. 6x = 14 – x
3. 7x = 14
4. x = 2
REASON
1. GIVEN
2. Multiplication Property
3. Addition Property
4. Division Property
It will give you the 1st stepFirst reason is always “given”
Given: 3x = 7 – 1/2x Prove: x = 2
It will give you the last step!
Step
1. 2x + 3 = 11
2. 2x = 8
3. x = 4
Reason
1. Given
2. Subtraction Property
3. Division Property
Write a Geometric Proof
If A B, mB = 2mC, and mC = 45, then mA = 90. Write a two-column proof to verify this conjecture.
5. mA = 90 5. Simplify
Statements ReasonsProof:
4. Substitution4. mA = 2(45)
Write a Geometric Proof
2. mA = mB 2. Definition of angles
1. Given1. A B; mB = 2mC; mC = 45
3. Transitive Property of Equality
3. mA = 2mC
Statements ReasonsProof:
1. Given1.
2. 2. _______________?
3. AB = RS 3. Definition of congruent segments
4. AB = 12 4. Given
5. RS = 12 5. Substitution
A. Reflexive Property of Equality
B. Symmetric Property of Equality
C. Transitive Property of Equality
D. Substitution Property of Equality
Homework
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