Transcript Chapter 2 - Juan Diego Academy

2-5 Algebraic proofs
SAT Problem of the day
 The volume and surface area of a cube are equal.
 What is the length of an edge of this cube?
 A) 1
 B) 2
 C)4
 D)6
 E)9
SAT problem of the day
 Answer :D
Objectives
* Review properties of equality and use them to
write algebraic proofs.
*Identify properties of equality and congruence.
What are Proofs?
 A proof 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 justifications to show that every
step is valid.
Properties
Properties
 The Distributive Property states that:
 a(b + c) = ab + ac.
Example#1
 Solve the equation 4m – 8 = –12. Write a
justification for each step.
 4m – 8 = –12
 +8
+8
Equality
 4m
= –4
Given equation
Addition Property of
Simplify.
Division Property of Equality
m =
–1
Simplify.
Example#2
 Solve the equation
. Write a
justification for each step.
Given equation
Multiplication Property of Equality.
t = –14
Simplify.
Example#3
 Given: 3 𝑥
 Prove: x=2
5
−
3
=1
Example#4
 Given: 7(2𝑥 + 1) = 63
 Prove: x=4
Student Guided Practice
Do problems 2-7 on your book page 107
Applications
 What is the temperature in degrees
Fahrenheit F when it is 15°C? Solve the
9
equation F =
C + 32 for F and justify
each step.
5
Applications
 What is the temperature in degrees Celsius
C when it is 86°F? Solve the equation C =
5/9(F – 32) for C and justify each step.
Algebraic proofs in geometry
 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.
Properties
A ____________ B
 AB represents the length AB, so you can think of
AB as a variable representing a number.
Geometric properties
 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#5
 Write a justification for each step.
NO = NM + MO
Example#6
 Write a justification for each step.
mABC = mABD + mDBC
Student Guided Practice
 Do Problems 10 and 11 from page 107 on your book
Homework!!
 Do problems 16-23 from page 108
Closure
 Today we learned about algebraic proofs and how to
justify each step.
 Next class we are going to learned about geometric
proofs