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 midpointDefinition of angle bisectorAngle Addiction PostulateSegment 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