2.6 Algebraic Proof

1. 2.6 Algebraic Proof

2. Objectives • Use algebra to write two-column proofs • Use properties of equality in geometry proofs

3. ALGEBRAIC PROPERTIES OF EQUALITY Reflexive Property a = a. Symmetric Property If a = b, then b = a. Addition Property of Equality If a = b, then a + c = b + c. Subtraction Property of Equality If a = b, then a – c = b – c. Multiplication Property of Equality If a = b, then ac = bc. Division Property of Equality If a = b, then a/c = b/c. Transitive Property of Equality If a = b and b = c, then a = c. Distributive Property a(b + c) = ab + ac. Substitution Property of Equality If a = b, then you may replace b with a in any expression.

4. Two-Column Proof • Two-Column Proof – A proof format used in geometry in which an argument is proven with statements and reasons (facts, definitions, rules).

5. Proof: Statements Reasons Two-Column Proof

6. Proof: Statements Reasons Example 1: Write a two column proof: Given: 2(x+3) = 24 Prove: x = 9

7. If Write a two-column proof. then Proof: Statements Reasons Example 2:

8. Write a two-column proof for the following. Example 3:

9. Given: m leg 1 22 cm Prove: m leg 3 22 cm Example 4: SEA LIFE A starfish has five legs. If the length of leg 1 is 22 centimeters, and leg 1 is congruent to leg 2, and leg 2 is congruent to leg 3, prove that leg 3 has length 22 centimeters.

10. Proof: Statements Reasons 1. 1. 2. 2. 3. m leg 1 m leg 3 3. 4. m leg 1 22 cm 4. 5. m leg 3 22 cm 5. Example 4:

11. Assignment • Geometry, pgs. 32-34