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ella [17]
3 years ago
9

Explain the purpose of statements and reasons in a formal proof.

Mathematics
1 answer:
baherus [9]3 years ago
3 0

Geometric proofs can be written in one of two ways: two columns, or a paragraph. A paragraph proof is only a two-column proof written in sentences. However, since it is easier to leave steps out when writing a paragraph proof, we'll learn the two-column method.

A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column. Every step of the proof (that is, every conclusion that is made) is a row in the two-column proof.

Writing a proof consists of a few different steps.

Draw the figure that illustrates what is to be proved. The figure may already be drawn for you, or you may have to draw it yourself.

List the given statements, and then list the conclusion to be proved. Now you have a beginning and an end to the proof.

Mark the figure according to what you can deduce about it from the information given. This is the step of the proof in which you actually find out how the proof is to be made, and whether or not you are able to prove what is asked. Congruent sides, angles, etc. should all be marked so that you can see for yourself what must be written in the proof to convince the reader that you are right in your conclusion.

Write the steps down carefully, without skipping even the simplest one. Some of the first steps are often the given statements (but not always), and the last step is the conclusion that you set out to prove. A sample proof looks like this:

Given:

Segment AD bisects segment BC.

Segment BC bisects segment AD.

Prove:

Triangles ABM and DCM are congruent.

Notice that when the SAS postulate was used, the numbers in parentheses correspond to the numbers of the statements in which each side and angle was shown to be congruent. Anytime it is helpful to refer to certain parts of a proof, you can include the numbers of the appropriate statements in parentheses after the reason.

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Tim installs 50 square feet of his floor in 45 minutes. At this rate, how long does it take him to install 495 square feet?
77julia77 [94]

Answer:

99.5 minutes

Step-by-step explanation:

50=45

495=?

495×45÷50=99.5

6 0
3 years ago
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How do I use the subtraction theorem to write equivalent expressions?
Andreas93 [3]
The subtraction theorem states that for all real numbers, a and b, a-b=a+(-b).
(To subtract, we can add the inverse.)
Thus, we can have the these two equivalent expressions.

3 - 2 = 3 + (-2) = 1\\ \\ 5 - (-2) = 5 + 2 = 7


3 0
3 years ago
The ratio of Victors money to Susies money is 4:7 at first. After Victor spent half of his money and Susie spent $60, Susie had
valkas [14]

Answer:

Victor originally had $80

Step-by-step explanation:

Let Victor have $4x

Let Susie have $7x

Since Victor spent half his money, he now has $2x

Susie spent $60 and thus now has $(7x - 60)

The final ratio of Victor's money to Susie's money is therefore  2x : $(7x - 60). This is given 1:2. Now we just need to solve the proportion by cross-multiplying

2x : (7x - 60) = 1:2

1 × (7x - 60) = 2 × 2x

7x - 60 = 4x

3x = 60

x = 20

Therefore Victor originally had $4x = $80.

7 0
2 years ago
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How do I solve this I’m dumb
laila [671]
-1/4 + f/8 = 1/2.
The LCD is 8.  Rewrite this equation as    -8/4 + 8f/8 = 8(1/2) and then reduce the result:

-2 + f = =4

Then f = 6.

You should check this result.

8 0
3 years ago
Ed wants to borrow $20,000 from a bank to open a small gym. Three banks charge different interest rates. To help decide the best
Delicious77 [7]

Answer:

First bank = $6792

City bank = $6803

Star bank = $6817  

Step-by-step explanation:

The lists of banks and their annual interests rates are attached.

For first bank, since the interest is 7.5%, The total interest = 7.5% of $20000 = 0.075 × $20000 = $1500

For city bank, since the interest is 8.2%, The total interest = 8.2% of $20000 = 0.082 × $20000 = $1640

For Star bank, since the interest is 9%, The total interest = 9% of $20000 = 0.09 × $20000 = $1800  

The loan plus interest for the banks annually are:

First bank = $20000 + $1500 = $21500

City bank = $20000 + $1640 = $21640

Star bank = $20000 + $1900 = $21900

The monthly payments for the banks are:

First bank = $21500 / 12 months = $1792

City bank = $21640 / 12 months = $1803

Star bank = $21800 / 12 months = $1817

Since The cost to run the gym each month is $5,000. Ed's total monthly expenses for each loan option = monthly payments + cost for each month. It is calculated as:

First bank = $5000 + $1792 = $6792

City bank = $5000 + $1803 = $6803

Star bank = $5000 + $1817 = $6817  

3 0
3 years ago
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