If an organism is a parasite, then it survives by living on or in a host organism. If a parasite lives in or on a host organism, then it harms its host. What conclusion can you draw if an organism is a parasite? Problem of the Day

Section 2-6 Algebraic Proof

Then Now Objectives You used postulates about points, lines, and planes. Use algebra to write two column proofs. Use properties of equality to write geometric proofs.

Common Core State Standards Content Standards Preparation for G.CO. 9 – Prove theorems about lines and angles. Mathematical Practices 3) Construct viable arguments and critique the reasoning of others. Common Core State Standards

Properties of Real Numbers

Proof: a logical argument in which each statement you make is supported by a statement that is accepted as true. Algebraic Proof: a proof that is made up of a series of algebraic statements. Vocabulary

State the property that justifies each statement State the property that justifies each statement. If 4 + (– 5) = – 1, then x + 4 + (– 5) = x – 1 Example 1

State the property that justifies each statement. If 5 = y, then y = 5 Example 1

Prove that if 2x – 13 = –5, then x = 4 Prove that if 2x – 13 = –5, then x = 4. Write a justification for each step. Example 1

A two-column proof or formal proof contains statements and reasons organized in two columns. Vocabulary

Write a two column proof to verify: If 5𝑥+1 2 −8=0, then x = 3. Example 2

If the distance d an object travels is given by d = 20t + 5, the time t that the object travels is given by t= 𝑑−5 20 . Write a two-column proof to verify this conjecture. Example 2

If two segments are congruent, you can say their lengths are equal (or vice versa). If 𝐴𝐵 ≅ 𝐶𝐷 , then AB = CD OR If AB = CD, then 𝐴𝐵 ≅ 𝐶𝐷 Both reasons would be: Definition of congruent segments Congruency

Likewise, if two angles are congruent, you can say their measures are equal. If ∠EFG ≅ ∠HIJ, then m∠EFG = m∠HIJ OR If m∠EFG = m∠HIJ, then ∠EFG ≅ ∠HIJ Both reasons would be: Definition of congruent angles Congruency

Properties of Equality

Write a two column proof to verify the conjecture. Example 3

Write a two column proof to verify the conjecture. Example 3

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