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HW- pgs. 107-108 (2-5, 11-15, 25-28, 30-32)
Ch. 2 Test THURSDAY 10-10-13
www.westex.org HS, Teacher Websites
10-3-13
Warm up—Geometry CPA
Solve each equation.
1. 4t – 7 = 8t + 3
2. 2(y – 5) – 20 = 0
GOAL:
I will be able to:
1. review properties of equality and use them to
write algebraic proofs.
2. identify properties of equality and congruence.
HW- pg. 107-108 (2-5, 11-15, 25-28, 30-32)
Ch. 2 Test THURSDAY 10-10-13
www.westex.org
HS, Teacher Websites
Name _________________________
Geometry CPA
2-5 Algebraic Proof
GOAL:
I will be able to:
1. review properties of equality and use them to write algebraic proofs.
2. identify properties of equality and congruence.
Date ________
A _______________ is an argument that uses logic, definitions, properties, and previously
proven statements to show that a conclusion is true.
An important part of writing a proof is giving ___________________ to show that every
step is valid.
Example 1: Solving an Equation in Algebra
Solve the equation 4m – 8 = –12. Write a justification for each step.
STATEMENT
REASON
4m – 8 = –12
You Try:
Solve the equation
STATEMENT
1
t  7 . Write a justification for each step.
2
REASON
1
t  7
2
Like algebra, geometry also uses numbers, variables, and operations. For example, segment
lengths and angle measures are numbers. So you can use these same properties of equality to
write algebraic proofs in geometry.
Example 2: Solving an Equation in Geometry
Write a justification for each step.
STATEMENT
NO = NM + MO
4x – 4 = 2x + (3x – 9)
4x – 4 = 5x – 9
–4 = x – 9
5=x
REASON
____________________
____________________
____________________
____________________
____________________
You Try:
Write a justification for each step.
STATEMENT
mABC = mABD + mDBC
8x° = (3x + 5)° + (6x – 16)°
8x = 9x – 11
–x = –11
x = 11
REASON
____________________
____________________
____________________
____________________
____________________
You learned in Chapter 1 that segments with equal lengths are congruent and that angles with
equal measures are congruent. So the Reflexive, Symmetric, and Transitive Properties of
Equality have corresponding properties of congruence.
Example 3: Identifying Property of Equality and Congruence
Identify the property that justifies each statement.
A. QRS  QRS
B. m1 = m2 so m2 = m1
C. AB  CD and CD  EF , so AB  EF .
D. 32° = 32°
You Try:
Identify the property that justifies each statement.
1. DE = GH, so GH = DE.
2. 94° = 94°
3. 0 = a, and a = x. So 0 = x.
4. A  Y, so Y  A
EXIT TICKET
Name _______________________ 10-3-13
Which properties of equality have corresponding properties of congruence.
EXIT TICKET
Name _______________________ 10-3-13
Which properties of equality have corresponding properties of congruence.
EXIT TICKET
Name _______________________ 10-3-13
Which properties of equality have corresponding properties of congruence.
EXIT TICKET
Name _______________________ 10-3-13
Which properties of equality have corresponding properties of congruence.
EXIT TICKET
Name _______________________ 10-3-13
Which properties of equality have corresponding properties of congruence.