Section 2-4: Reasoning in Algebra

Section 2-4: Reasoning in Algebra Goal 2.01: Use logic and deductive reasoning to draw conclusions and solve problems.

Turn in Homework • Lesson Quiz 2-3

Essential Question How are properties of equality used in Algebraic and Geometric Proofs?

Addition Property of Equality If a = b and c = d, then a + c = b + d.

subtraction property of equality If a = b and c = d, then a – c = b – d.

multiplication property of equality If a = b then ac = bc.

division property of equality If a = b and c ≠ 0, then a = b . c c

substitution property If a = b then either a or b may be substituted for the other in any equation or inequality.

reflexive (identity) Property a = a DE = DE  1 =  1

Symmetric Property If a = b then b = a.

Distributive Property a ( b + c ) = ab + ac a ( b – c) = ab - ac

Transitive Property If a = b and b = c, then a = c. If DE = FG and FG = JK, then DE = JK. If 1 = 2 and 2=3, then 1 = 3.

Midpoint Theorem If M is the midpoint of AB, then AM = ½ AB and MB = ½ AB, also 2 AM = AB and 2MB = AB.

Angle Bisector Theorem If BX is the bisector of  ABC, then 2 m ABX = m ABC and m ABX = m ABC. 2 m XBC = m ABC and m XBC = m ABC.

Review: Definition of midpoint Definition of angle bisector Angle Addiction Postulate Segment Addition Postulate

Compare the definition of midpoint to the Midpoint Theorem?

Compare the definition of the angle bisector and the Angle Bisector Theorem?

Examples • Worksheet Labeled: Justify the Statements examples • Together: p 92 (5 – 24 all)

Group Work Practice 2-4 2 – 14 evens

Individual Work Practice 2-4: 1 – 13 odds

Assess Lesson Quiz 2 – 4: for a grade

Homework Worksheet back on Front: Labeled: Properties of Algebra Justify the Statement Homework

Section 2-4: Reasoning in Algebra