To the video! Important Properties for Proofs

Name______________________

[PACKET 2.3: WRITING PROOFS] 1

Write your questions here!

More proofs! This time, no "fill in the blanks."

To the video!

Important Properties for Proofs

Addition Property

Reflexive Property

Substitution Property

Subtraction Property

Symmetric Property

Combining Like Terms

Multiplication Property

Transitive Property

Simplification

Division Property

Distributive Property

All right angles @

Angle Addition Postulate

Vertical Angles are @

Segment Addition Postulate

"Definition of___________" (Bisector, Midpoint, Complementary, Supplementary, etc.)

Example #1

This list will grow as we continue through Geometry this year.

Directions: Complete the following proofs.

Statement

Given: -100 ? (4x ? 2) = -94 Prove: x = -1

Reason

1.

1.

2.

2.

3.

3.

4.

4.

5.

5.

Remember, the first statement will always be the given while the last statement should always be what you need to prove.

Example #2

2 PACKET 2.3: WRITING PROOFS

Write your questions here!

m

1 4

2 3

Given: 1 4 Prove: 2 3

Example #3

3

Given: 2 5 Prove: 4 8

2

1.

2. 3. 4.

5. 6.

1

Given: Prove:

1 and 2 are supplementary 2 and 3 are supplementary 1 3

1. 2. 3. 4. 5. 6.

Example #4

[PACKET 2.3: WRITING PROOFS] 3

Solve each equation for x!

Multiply!

1. 12x ? 3 = -3 2.

5x + -2 = 3x - 4 3.

2x(2x ? 1)

Factor!

4. 3x2 ? 12x

5. Graph the equation:

y = 4 - x

6. Graph the equation:

x = -3

Proof #1

Practice 2.3: Writing Proofs

Support each statement by writing a conclusion with a valid reason.

1. Given:

2x = 72

2. Given:

. 3.

Given:

X is the midpoint of

Conclusion: _________________ Conclusion: ____________

Conclusion:

______________

Reason:_________________

Reason:_________________

Reason:_________________

Directions: Complete the following proofs.

Given: 10x + 4 = 44

Statement

1. 2. 3 .

Prove: x = 4

Reason

1. 2. 3.

Given: 10x + 42 = 20 ? x

Statement

1. 2. 3. 4.

Prove: x = -2

Reason

1. 2. 3. 4.

Proof #4

Proof #2

Given: 1 - x = 11

Statement

1. 2. 3.

Prove: x = -10

Reason

1. 2. 3.

Given: 6x - (4x ? 1) = 2

Statement

1. 2. 3. 4. 5.

Prove: x = ?

Reason

1. 2. 3. 4. 5.

Proof #3

4 PACKET 2.3: WRITING PROOFS

Proof #5

Given: 13 ? 4(x ? 2) - 41 = 0

Statement

1. 2. 3. 4. 5. 6.

Prove: x = -5

Reason

1. 2. 3. 4. 5. 6.

Application 2.3: Introduction To Proofs

Proof #1

Given: -3(4 ? x) = 12

Statement

1. 2. 3 . 4.

Prove: x = 8

Reason

1. 2. 3. 4.

Support each statement by writing a conclusion with a valid reason.

2. Given:

30x = 300

Conclusion: ____________

Reason: _______________

Proof #3

Given: b g Prove: f c

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