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