approved MATH 47524Y-8 intro to proofs packet

Name______________________
[PACKET 2.2: INTRO TO PROOFS] 1
Write your questions here!


A__________________, is a convincing argument that uses deductive
reasoning. Every statement you make must be justified with a valid property. The
following properties will be super valuable:

Property Example
If you are given: x – 5 = 12

Then you can conclude:
If you are given: x + 6 = 15

Then you can conclude:
If you are given: ⅕x = -2

Then you can conclude:
If you are given: 2x = 8

Then you can conclude:
If you are given: y = 2x + 2 and x = 5

Then you can conclude:
Other Important Properties
If you are given: 30

Then you can conclude:
If you are given: 5=x

Then you can conclude:
If you are given: y = j and j = -13

Then you can conclude:
If you are given: 12 = 3(x – 9)

Then you can conclude:
If you are given: y = 3(4) - 12

Then you can conclude:
If you are given: 100 = 45x – 20x

Then you can conclude:

The Algemazing-Postulate* Always conclude: 𝐶𝑜𝑜𝑙𝑛𝑒𝑠𝑠 '()*+,-. > 𝐶𝑜𝑜𝑙𝑛𝑒𝑠𝑠(1-,(2)


*
The last postulate has yet to be proven, but the teachers of this course are pretty sure it’s true based on how highly we think of
ourselves. We are currently refusing outside input regarding this postulate.



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, Write your questions here! 2 PACKET 2.2: INTRO TO PROOFS

Tell which property justifies each conclusion.

1. Given: 6x + 2 = 12 2. Given: 45 = x
Conclusion: 6x = 10 Conclusion: x = 45


3. Given: 3x – 7x = 20 4. Given: 4(q - x) = r
Conclusion: -4x = 20° Conclusion: 4q - 4x = r


5. If a = r and r = 60°, 6. If B is the midpoint of 𝐺𝐻,
then a = 60°. then…_______________
(???)
2 Column Proofs

A two-column proof lists each statement on the left with a justification on the right.
Each step follows logically from the line before it.

Fill in the missing statements or reasons for the following two-column proof.

Given: 45 + 2(x -10) = 85 ß This line tells you everything that has been ________, or everything that is known to be true.
Prove: x = 30
ß This line tells you what you must ________.

Statement Reason

1. 45 + 2(x -10) = 85 1.
Example #1




2. 2(x -10) = 40 2.
3. 2x - 20 = 40 3.
4. 2x = 60 4.
5. x = 30 5.



Given: 4x – 2(2 –x) = 4x -24
Prove: x = -10

Statement Reason

1. 1.
Example #2




2. -2(2 –x) = -24 2.

3. 2 – x = 12 3.
4. -x = 10 4.
5 5.
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