Free Printable Algebraic & Geometric Proofs

1.

If we know that two lines are parallel then we can conclude that their corresponding angles are equal because the....

a)

Angle Congruence Theorem

b)

Transitive Property

c)

Corresponding Angles Postulate

2.

If t=m and m=b, then we know that t=b because the.....

a)

Symmetric Property

b)

Transitive Property

c)

Definition of a Midpoint

d)

Reflexive Property

3.

M is the midpoint of segment PQ,

we know that segment PM = segment MQ,

because the...

a)

Definition of a Midpoint

b)

Segment Congruence Theorem

c)

CPCF Theorem

4.

We know that the m∠1 = m∠3, because the......

a)

Definition of Congruence

b)

Angle Congruence Theorem

c)

Vertical Angles Theorem

d)

Linear Pair Theorem

5.

We know that ∠1 & ∠4 are supplementary because the...

a)

Linear Pair Theorem

b)

Definition of Supplementary Angles

c)

Definition of Complimentary Angles

6.

Ray KM is an angle bisector to ∠LKJ,

therefore m∠LKM = m∠MKL because the.....

a)

Angle Congruence Theorem

b)

Corresponding Angles Postulate

c)

Symmetric Property

d)

Definition of an Angle Bisector

7.

Which reason justifies the statement?

a)

Subtraction Property of Equality

b)

Combine Like Terms

c)

Division Property of Equality

d)

Addition Property of Equality

8.

Which reason justifies the statement?

a)

Addition Property of Equality

b)

Multiplication Property of Equality

c)

Subtraction Property of Equality

d)

Division Property of Equality

9.

Which reason justifies the statement?

a)

Division Property of Equality

b)

Addition Property of Equality

c)

Multiplication Property of Equality

d)

Subtraction Property of Equality

10.

Which reason justifies the statement?

a)

Combine Like Terms

b)

Multiplication Property of Equality

c)

Division Property of Equality

d)

Addition Property of Equality

11.

Which reason justifies the statement?

a)

Combine Like Terms

b)

Distributive Property of Equality

c)

Multiplication Property of Equality

d)

Division Property of Equality

12.

Which reason justifies the statement?

a)

Reflexive Property of Equality

b)

Division Property of Equality

c)

Symmetric Property of Equality

d)

Commutative Property of Equality

13.

Which reason justifies the statement?

a)

Subtraction Property of Equality

b)

Combine Like Terms

c)

Addition Property of Equality

d)

Substitution Property of Equality

14.

Name the property of equality or congruence that justifies going from the first statement to the second statement.

a)

Associative Property

b)

Commutative Property

c)

Distributive Property

d)

Combine Like Terms

15.

What is step 2?

a)

Distributive Property

b)

Multiplication property of equality

c)

Division property of equality

d)

Substitution property

16.

What is step 6?

a)

Subtraction property of equality

b)

Division property of equality

c)

Addition property of equality

d)

Given

17.

What is step 2?

a)

Given

b)

Subtraction Property of Equality

c)

Division Property of Equality

d)

Multiplication Property of Equality

e)

Addition Property of Equality

18.

Step 1 is what

a)

addition property of equality

b)

given

c)

subtraction property of equality

d)

prove

19.

What is reason 3?

a)

Addition Property of Equality

b)

Subtraction Property of Equality

c)

Multiplication Property of Equality

d)

Division Property of Equality

20.

What is reason 5?

a)

Transitive Property

b)

Reflexive Property

c)

Symmetric Property

d)

Prove

21.

What is reason 3?

a)

Addition Property of Equality

b)

Subtraction Property of Equality

c)

Multiplication Property of Equality

d)

Division Property of Equality

22.

If 80 = m∠A, then m∠A = 80

a)

Reflexive PoE

b)

Symmetric PoE

c)

Transitive PoE

d)

Distributive Property

23.

What is always the 1st reason of a proof?

a)

Given

b)

Reason

c)

Prove

d)

Statement

24.

Fill in the missing steps

a)

4x = 28

b)

Distributive Prop

c)

Addition Prop

d)

Prove

e)

4x + 8 - 8 = 36 - 8

f)

Simplify

g)

Division Prop

h)

x = 7

1

2

3

4

1)

2)

3)

4)

25.

Given: 5(x+2) = -3x-6

Prove: x = -2

a)5(x+2) = -3x-6

b)5x+10 = -3x-6

c)8x+10 = -6

d)8x = -16

e)x = -2

f)Given

g)Distributive Property

h)Addition Property

i)Subtraction Property

j)Division Property

1

2

3

4

5

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7

8

9

10

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

26.

Given: 4x+9 = 16-3x

Prove: x = 1

a)4x+9 = 16-3x

b)7x+9 = 16

c)7x = 7

d)x = 1

e)Given

f)Addition Property

g)Subtraction Property

h)Division Property

i)Distributive Property

j)Multiplication Property

1

2

3

4

5

6

7

8

1)

2)

3)

4)

5)

6)

7)

8)

27.

Given: 4+2(3x+5) = 11-x

Prove: $\frac{-3}{7}$

a)4+6x+10 = 11-x

b)Distributive Property

c)6x+14 = 11-x

d)Simplify

e)7x+14 = 11

f)Addition Property

g)7x = -3

h)Subtraction Property

i)x = -3/7

j)Division Property

1

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3

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7

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9

10

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

28.

Given: $\frac{-5x+2}{7}=\ -4$

Prove: x = 6

a)

\frac{-5x+2}{7}=-4

b)-5x+2 = -28

c)-5x = -30

d)x = 6

e)Given

f)Multiplication Property

g)Subtraction Property

h)Division Property

i)Addition Property

j)Simplify

1

2

3

4

5

6

7

8

1)

2)

3)

4)

5)

6)

7)

8)

29.

Given: 17-3(w+5) = 6(w+5)-2w

Prove: w = -4

a)17-3w-15 = 6w+30-2w

b)-3x+2 = 4w+30

c)-7w+2 = 30

d)-7w = 28

e)Distributive Property

f)Simplify

g)Subtraction Property

h)Subtraction Property #2

i)w = -4

j)Division Property

1

2

3

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7

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9

10

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

30.

Fill in the proof.

Given: 3(2x - 6) = x + 7

Prove: x = 5

a)

Division

b)

x = 5

c)

Addition

d)

5x = 25

e)

Subtraction

f)

5x - 18 = 7

g)

3(2x - 6) = x + 7

h)

Given

i)

6x - 18 = x + 7

j)

Distributive

1

2

3

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5

6

7

8

9

10

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

31.

Given: 3x+12 = 8x-18

Prove: x = 6

a)3x+12 = 8x-18

b)Given

c)12 = 5x-18

d)Subtraction Property

e)30= 5x

f)Addition Property

g)6 = x

h)Division Property

i)x = 6

j)Symmetric Property

1

2

3

4

5

6

7

8

9

10

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

32.

Given: 3(5x+1) = 13x+5

Prove: x = 1

a)3(5x+1) = 13x+5

b)Given

c)15x+3 = 13x+5

d)Distributive Property

e)2x+3 = 5

f)2x = 2

g)Subtraction Property

h)Subtraction Property #2

i)Division Property

j)x = 1

1

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9

10

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

33.

Given: 7y-84 = 2y+61

Prove: y = 29

a)7y-84 = 2y+61

b)Given

c)5y-84 = 61

d)Subtraction Property

e)5y = 145

f)Addition Property

g)Division Property

h)y = 29

i)Distributive Property

j)5y = 23

1

2

3

4

5

6

7

8

1)

2)

3)

4)

5)

6)

7)

8)

34.

Given: 6r-3 = -2(r+1)

Prove: r = $\frac{1}{8}$

a)6r-3 = -2(r+1)

b)Given

c)6r-3 = -2r-2

d)Distributive Property

e)8r-3 = -2

f)Addition Property

g)8r = 1

h)Addition Property #2

i)r = 1/8

j)Division Property

1

2

3

4

5

6

7

8

9

10

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

35.

Given: 4(5x+7)-3x = 12x-27

Prove: x = -11

a)Given

b)Distributive Property

c)17x+28 = 12x-27

d)5x+28 = -27

e)5x = -55

f)Division Property

g)Addition Property

h)32x+28 = 27

i)5x = 1

1

2

3

4

5

6

1)

2)

3)

4)

5)

6)

36.

Given: 11 = 3(x-4)+2

Prove: x = 7

a)11 = 3x-12+2

b)Distributive Property

c)11 = 3x-10

d)Combine Like Terms

e)21 = 3x

f)Addition Property

g)7 = x

h)Division Property

i)x = 7

j)Symmetric Property

1

2

3

4

5

6

7

8

9

10

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

37.

a)

a. Segment Addition Postulate b. Substitution Property c. Simplify

b)

a. Definition of Midpoint b. Substitution Property c. Simplify

c)

a. Segment Addition Postulate b. Symmetric Property c. Simplify

d)

a. Definition of Bisect b. Substitution Property c. Simplify

38.

a)

a. Symmetric Property b. Angle Addition Postulate c. Substitution Property d. Angle Addition Postulate e. Subtraction

b)

a. Reflexive Property b. Addition Property c. Angle Addition Postulate d. Angle Addition Postulate e. Substitution Property

c)

a. Reflexive Property b. Transitive Property c. Angle Addition Postulate d. Angle Addition Postulate e. Substitution Property

39.

What is the best REASON 2 ?

a)

Symmetric Property

b)

Reflexive Property

c)

Distributive Property

d)

Transitive Property

40.

Which is the best REASON 1 ?

a)

Given

b)

Definition of Midpoint

c)

Definition of Bisect

d)

Reflexive Property

41.

Which is the best choice for STATEMENT 2 ?

a)

DE = EF

b)

DE = DF

c)

EF = DF

d)

EF=EF

42.

Which is the best choice for REASON 3 ?

a)

Reflexive Property

b)

Transitive Property

c)

Symmetric Property

d)

Addition Property

43.

Which is the best choice for STATEMENT 2 ?

a)

$\angle1\ and\ \angle2\ are\ complementary$

b)

$\angle1\ and\ \angle2\ are\ vertical\ angles$

c)

$\angle1\ and\ \angle2\$ are supplementary

d)

$\angle1\ and\ \angle2\ are\ congruent$

44.

Which is the best choice for REASON 3 ?

a)

Definition of Supplementary

b)

Definition of Complementary

c)

Definition of Congruence

d)

Definition of Convex

45.

Fill in the blanks for the proof.

a)

Substitution

b)

Addition Property of Equality

c)

Segment Addition Postulate

d)

2x + 3x - 9 = 4x - 4

e)

Simplify

f)

x - 9 = -4

1

2

3

4

5

6

1)

2)

3)

4)

5)

6)

46.

Fill in the blanks of the proof.

a)

Simplify

b)

2AB = AC

c)

AB + BC = AC

d)

B is the midpoint of segment AC

e)

AB = BC

f)

Definition of midpoint

g)

Given

1

2

3

4

5

6

7

1)

2)

3)

4)

5)

6)

7)

47.

Match the REASONS with the STATEMENTS.

a)

Reflexive property

b)

Addition property

c)

Linear pair

d)

Def of congruent angles DOCA

e)

Given

f)

Def of angle bisector

g)

Vertical angles

h)

Transitive property

1

2

3

4

5

1)

2)

3)

4)

5)

48.

Complete the Proof with the given labels. The givens have been labeled for you.

a)

Def of Congruent Angles

b)

Subtraction

c)

Reflexive

d)

Given (1)

e)

Given (3)

f)

Def of Complementary Angles

g)

Substitution

1

2

3

4

5

6

7

1)

2)

3)

4)

5)

6)

7)

Algebraic & Geometric Proofs

Total questions: 48

Worksheet time: 3hrs 40mins

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