Download Simplify. - Ms. Huls

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2.5: Algebraic Proof
Learning Objective
 SWBAT
review properties of equality and use
them to write algebraic proofs.
 Identify
properties of equality and
congruence.
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Today is the Big P Day!!!
 Take
out your homework
 Take
out your whiteboard marker
 If
you do not have one, ASK me. Do not
borrow a friends (unless they have two)
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Math Joke of the Day
Why was the math book
sad?
Because it had too many
problems
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Whiteboards
1.
1.
Find the measure of segment HJ.
Find the measure of <WXZ.
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2.5 Algebraic Proofs
Our goal for today is to answer the following
guiding question:

Why is it important to justify the steps in a
proof with reasons?
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Proof
Proof

argument that uses logic,
definitions, properties, and
previously proven statements to
show that a conclusion is true.
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Important
You
must give justifications to show
that every step is valid
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Remember!
The Distributive Property states that
a(b + c) = ab + ac.
Example
1: Solving
an Equation in Algebra
EXAMPLE
1
Solve the equation 4m – 8 = –12. Write a
justification for each step.
4m – 8 = –12
+8
+8
Given equation
Addition Property of Equality
4m
Simplify.
= –4
Division Property of Equality
m = –1
Simplify.
EXAMPLE 2
Solve the equation
each step.
. Write a justification for
Given equation
Multiplication Property of Equality.
t = –14
Simplify.
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EXAMPLE 3
 What
is the temperature in degrees
Fahrenheit F when it is 15°C? Solve the
equation F = C + 32 for F and justify each
step.
Given equation
Substitution Property of Equality
F = 27 + 32
F = 59
F = 59°
Simplify.
Simplify.
EXAMPLE 42: Solving an Equation in Geometry
Write a justification for each step.
NO = NM + MO
Segment Addition Post.
4x – 4 = 2x + (3x – 9) Substitution Property of Equality
4x – 4 = 5x – 9
–4 = x – 9
5=x
Simplify.
Subtraction Property of Equality
Addition Property of Equality
EXAMPLE 52: Solving an Equation in Geometry
Write a justification for each step.
mABC = mABD + mDBC
 Add. Post.
8x° = (3x + 5)° + (6x – 16)° Subst. Prop. of Equality
8x = 9x – 11
–x = –11
x = 11
Simplify.
Subtr. Prop. of Equality.
Mult. Prop. of Equality.
Remember!
Numbers are equal (=) and figures are congruent
().
EXAMPLE 6
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°
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EXIT TICKET
Please do the following:

Clear your desk. All you need is a pencil and eraser.

You will be given 5 minutes to complete the check for
understanding questions.

This is a mini quiz.

NO TALKING

Please remember your name, period, and row #.
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1. Solve the equation. Write a justification for each
step.
6r – 3 = –2(r + 1)
2. Identify the property that justifies each statement.
(a)
(b)
(c)
x = y and y = z, so x = z.
DEF  DEF
AB  CD, so CD  AB.
3. Why is it important to justify the steps in a proof with
reasons?
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