Intro to Proofs Unit IC Day 2

Do now Solve for x 5x – 18 = 3x + 2

Theorems Recall: A postulate is a rule that is accepted without ___________ A theorem is a true statement that follows from _________________ ◦ All theorems must be ______________

Algebraic Properties of Equality Let a, b, and c be real numbers. Addition property: If a = b, then a + c = b + c. Subtraction property: If a = b, then a – c = b – c. Multiplication property: If a = b, then ac = bc. Division property: If a = b and c ≠ 0, then a/c = b/c.

Algebraic Properties of Equality Let a, b, and c be real numbers. Reflexive property: a = a. Symmetric property: If a = b, then b = a. Transitive property: If a = b and b = c, then a = c. Substitution property: If a = b, then a can be substituted for b in any equation or expression.

Example 1 Solve for x. Justify each step.

They work for geometry, too!

Definition of congruence Informal: Two geometric figures are congruent if they have the exact same size and shape. Definition: If two figures are congruent, then their ______________ are equal. ◦ Must use this to move between “ ≅ ” and “=” in a proof!

Types of Proof Two-column proof: statements in one column, reasons in the other Paragraph proof: statements and reasons in paragraph form Flow proof: statements and reasons arranged graphically with arrows showing direction of logic

Example 2

More Theorems Note: this is not the definition of a right angle— measure is 90º

Proof of Theorem 2.3

More Theorems More Theorems

Example 3

Closure Draw an example diagram in which  1 and  3 are both linear pairs with  2. Tell two ways you can prove m  1 = m  3.