1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ray Of Light [21]
2 years ago
14

How do I understand two column proofs?

Mathematics
1 answer:
Anna007 [38]2 years ago
7 0

Explanation:

When you solve an equation, you use the rules of algebra. Before you begin solving equations, you learn the rules of algebra. Specifically, you learn about rules relating to addition, multiplication, equality, identity elements, order of operations, and inverse operations.

Whenever you "show work" solving an equation, you are demonstrating at each step that you know how to apply these rules to get one step closer to a solution.

__

A 2-column proof is a list of "statements" in one column, and associated "reasons" in the other column.

The first statement is generally a list of all of the things that are "given" in the particular problem. The first reason is generally, "Given".

The last statement is generally a statement of what you are trying to prove. The last reason is a description of the postulate or theorem you used to conclude the last statement is true, based on the previous statement.

__

Here's a brief example:

Suppose we have line segment RT with point S on the segment. Suppose the lengths are given: RS = 3, ST = 4. We are asked to prove that RT = 7. The proof might look like this:

<u>Statement</u> . . . . <u>Reason</u>

Point S lies on RT; RS = 3; ST = 4 . . . . Given

RT = RS +ST . . . . segment addition postulate

RT = 3 + 4 . . . . substitution property of equality

RT = 7 . . . . properties of integers

__

So, creating or filling in 2-column proofs requires you have a good understanding of the theorems and postulates you are allowed (or expected) to choose from, and an understanding of logical deduction. Essentially, you cannot make a statement, even if you "know it is true", unless you can cite the reason why you know it is true. Your proof needs to proceed step-by-step from what you are given to what you want to prove.

It might be useful to keep a notebook or "cheat sheet" of the names and meanings of the various properties and theorems and postulates you run across. Some that seem "obvious" still need to be justified. X = X, for example, is true because of the <em>reflexive property of equality</em>.

It can be helpful to read and understand proofs that you see in your curriculum materials, or that you find online--not just skim over them. This can help you see what detailed logical steps are needed, and the sorts of theorems and postulates that are cited as reasons. It is definitely helpful to pay attention when new relationships among geometrical objects are being introduced. You may have to use those later in a proof.

_____

<em>Additional comment</em>

As in the above proof, you may occasionally run across a situation where you're asked to "justify" some arithmetic fact: 3+4=7 or 2×3=6, for example. I have never been quite clear on the justification that is appropriate in such cases. In the above, I have used "properties of integers", but there may be some better, more formal reason I'm not currently aware of. This is another example of the "obvious" needing to be justified.

You might be interested in
What is 1/3 of 1 i need help with this pls answer quickly
Solnce55 [7]

Answer:

<h2>The answer is 1/3. 1 divided by 3 is 1/3</h2>

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
What is 90% of $634?
stiks02 [169]
$570.60 because 90/100=.90 so multiply that with 634 with .90 you get 570.60
6 0
3 years ago
Read 2 more answers
The approximate volume of a sphere with a diameter of 10 centimeters is
Alexeev081 [22]

Answer: The volume is approximately 523.6 cm³.

Step-by-step explanation:

The formula for the volume of a sphere is V=4/3(3.14)r³

The radius is 5 cm, the you just have to multiply everything together.

5 0
3 years ago
سا (a) From the definition of derivatives determine dy÷dx if y = -2÷x​
harina [27]

Step-by-step explanation:

Given: y = -\dfrac{2}{x}

Derivative of a power function x^n:

\dfrac{d}{dx}(x^n) = nx^{n-1}

Therefore,

\dfrac{dy}{dx}=-2(-1)x^{-2} = \dfrac{2}{x^2}

3 0
3 years ago
NEED HELP FAST BRIANLEST
AVprozaik [17]

Answer:

\frac{1}{4}^{2}

Step-by-step explanation:

When you solve these two equations, you end up with the same answer of 1/16 or 0.0625

3 0
2 years ago
Other questions:
  • Please help for brainliest
    10·2 answers
  • Which inequality has infinitely many negative integer solutions
    10·1 answer
  • An internet company charges a one-time setup fee of $44.99 and a monthly fee of $29.99 for Internet service. The company is offe
    11·1 answer
  • The admission fee at the county fair is $2 for children and $4 for adults. on a certain day, 2000 people enter the fair and $500
    14·1 answer
  • A figure is dilated by a scale factor of 12. If the origin is the center of dilaton, what is the image of a vertex located at (3
    14·1 answer
  • PLEASE HELPP PLEASEE
    13·1 answer
  • I will branilest this the correct answer
    6·2 answers
  • There are 100 pennies in a dollar.What fraction of a dollar is 61 pennies?Write it as a fraction,as a decimal,and in word from.
    10·1 answer
  • Help me, please<br> i really need it
    10·2 answers
  • -3x-2+7x=10 please help
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!