NAME
DATE
PERIOD
Practice
Algebraic Proof
PROOF Write a two-column proof to verify each conjecture.
1. If mZABC + m^CBD = 90, mZABC = 3x - 5,
and mZCBD = X~t1, thenx = 27.
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2. FINANCE The formula for simple interest is I = prt, where 7 is interest, p is principal,
r is rate, and t is time. Solve the formula for r and justify each step.
a
Chapter 2
40
Glencoe Geometry
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NAME
DATE
PERIOD
Word Problem Practice
Algebraic Proof
1. DOGS Jessica and Robert each own the
same number of dogs. Robert and Gail
also own the same number of dogs.
Without knowing how many dogs they
own, one can still conclude that Jessica
and Gail each own the same number of
dogs. What property is used to make
this conclusion?
4. FIGURINES Pete and Rhonda paint
figurines. They can both paint 8
figurines per hour. One day, Pete
worked 6 hours while Rhonda worked 9
hours. How many figurines did they
paint that day? Show how to get the
answer using the Distributive Property.
2. MONEY Lars and Peter each have the
same amount of money in their wallets.
They went to the store together and
decided to buy some cookies, splitting
the cost equally. After buying the
cookies, do they still have the same
amount of money in their wallets? What
property is relevant to help you decide?
5. AGE William's father is eight years
older than 4 times William's age.
William's father is 36 years old.
a. Let x be William's age. Translate the
given information into an algebraic
equation involving x.
3. MANUFACTURING A company
manufactures small electronic
components called diodes. Each diode
is worth $1.50. Plant A produced 4443
diodes and Plant B produced 5557
diodes. The supervisor was asked what
the total value of all the diodes was.
The supervisor immediately responded
"$15,000." The supervisor would not
have been able to compute the value so
quickly if he had to multiply $1.50 by
4443 and then add this to the result
of $1.50 times 5557. Explain how you
think the supervisor got the answer so
quickly?
Chapter 2
b. Fill in the missing steps and
justifications for each step in finding
the value of x.
41
Statements
1. 4* + 8 = 36
Properties
1. Original
equation
2.
2. Subtraction
Property
3. 4x = 28
3.
4 i* _ 2 8
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4.
5.
5. Substitution
Property
Glencoe Geometry
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