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Practicing Reasons for a 2-column proof
Contributed by: Scott

The first 3 sides are fill in the blank

responses.  I did not abbreviate any words

except for POE (property of equality) so to get

the response marked "correct" you have to spell

it correctly.  I did not include POE for Substitution.

 

A nice feature of this program is that at the end, you can

go back and review your answers by clicking on

the darkened arrow in the upper right corner of

the screen.  There will be an X in the corner of any

problem that you missed.  Check it out. 

1.  ∡3 and ∡4 are complements.

 

2.  m∡3 + m∡4 = 90

 

3.  ∡1 ≅ ∡4

 

4.  m∡1 = m∡4

 

5.  m∡3 + m∡1 = 90

 

6.  ∡3 and ∡1 are complements.

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

1.  m∡1 + m∡2 = 180∘ 

     

2.  ∡4 ≆ ∡5

 

3.  ∡5 ≅ ∡1

 

4.  ∡4 ≅ ∡1

 

5.  m∡4 = m∡1

 

6.  m∡4 + m∡2 = 180

 

7.  ∡4 and ∡2 are supplements

1
2
7. 

4. 

5. 

6. 
2. 
3.               Given
1. 
4
5

1.  m∡1 + m∡2 = 180 

2.  m∡2 + m∡3 = 180

 

3.  m∡1 + m∡2 = m∡2 + m∡3

 

4.  m∡1 = m∡3

 

5.  ∡1 ≅ ∡3

 

1

4

2

3
1. 
2. 
3. 
4. 
5. 
Segment Addition
Addition POE

Which is the correct missing reason?

1.  AB + BC = CD + BC

2.  AB = CD

A                B                   C             D

Subtraction POE

Definition of between

1.  Given

2.___?_____

 

                                      B        C

 

                    

1.  AB = CD

2.  AB + BC = CD + BC

What is the correct missing reason?

Segment Addition
Addition POE
A                B                   C             D
Subtraction POE
Def. of midpoint

1.  Given

2.___?_____

 

                                      B        C

 

                    

1.  ∡DEF ≅ ∡FEG

2.  EF bisects ∡DEG

Def. of angle trisector
Angle Addition
What is the correct reason for statement #2?
 E
     D
F
Def. of congruent ∡'s
Def. of angle bisector
G

1.  Given

2.  __?__

What is the correct missing reason for the statement?
Segment  Addition
Angle Addition
1.  m∡DEF + m∡FEG = m∡DEG
 E
     D
F

Addition POE

Def. of angle bisector
G
1.  ____?_____

1.  m∡HED + m∡DEF = m∡DEF + m∡FEG

2.  m∡HED = m∡FEG

What is the correct missing reason for statement #2?
  Addition POE
 Angle Addition
 E
H
     D
F
Def. of angle trisector
Subtraction POE
G

1.  Given

2.  ___?_____

1.  m∡HED = m∡FEG

2.  m∡HED + m∡DEF = m∡DEF + m∡FEG

What is the correct missing reason for statement #2?

  Angle Addition

  Addition POE
 E
H
     D
F
Subtraction POE
Def. of angle trisector
G

1.  Given

2.  ___?_____

Def. of midpoint
Def. of between
What is the correct reason for statement #2?

1.  Q is the midpoint of PR

2.  PQ ≅ QR

P                       Q                     R
Def. of segment bisector
Def. of congruence
T

1. Given

2.  ___?___

Def. of midpoint
Def. of between
What is the correct reason for statement #2?

1.  PQ ≅ QR

2.  QT bisects PR

P                       Q                     R
Def. of segment bisector
Def. of congruence
T

1. Given

2.  ___?___

Def. of angle trisector
Def of segment trisector
What is the correct reason for statement #2?

1.   BE and CE trisect AD

2.   AB ≅ BC ≅ CD

A                 B            C          D
Def. of ≅ segments
None of these

1.  Given

2.  __?__

E
Def. of angle trisector
Def of segment trisector
What is the correct reason for statement #2?

1.    ∡AEB ≅ ∡BEC ≅ ∡CED

2.  BE and CE trisect ∡AED

 

A                 B            C             D
E
Def. of congruence
None of these

1.  Given

2.  __?__

What is the correct reason for statement #3?
Def. of congruent angles

Def. of right angle

1.  ∡D is a right angle

2.  ∡E is a right angle

3.  ∡D ≅ ∡E

D
 E

1.  Given

2.  Given

3.  __?__

Substitution
Right angles are ≅
What is the correct reason for statement #3?
Def. of congruent angles

Def. of straight angle

1.  ∡BDC is a straight angle

2.  ∡FEG is a straight angle

3.  ∡BDC  ≅ ∡FEG

B       D        C
∙F
Substitution
Straight angles are ≅
∙E

1.  Given

2.  Given

3.  __?__

∙G
What is the correct reason for statement #3?
Def. of congruent angles

Def. of right angle

1.  m∡D =90

2.  m∡E =90

3.  ∡D ≅ ∡E

D
E

1.  Given

2.  Given

3.  __?__

Substitution
Right angles are ≅
What is the correct missing reason for statement #2?

1.  m∡HED = 40

2.  m∡HED + m∡DEF = m∡HEF

3.   40 + m∡DEF = m∡HEF

  Addition POE

  Angle Addition

 E
H
     D
F
Def. of congruent angles
Substitution POE
G

1.  Given

2.  ___?_____

3.  ___?_____

1.  m∡HED = 40

2.  m∡HED + m∡DEF = m∡HEF

3.   40 + m∡DEF = m∡HEF

What is the correct missing reason for statement #3?
  Addition POE

  Angle Addition

 E
H
     D
F
Def. of congruent angles
Substitution POE
G

1.  Given

2.  ___?_____

3.  ___?_____

1.  AB = EF

2.  AB + BC = AC

3.  EF + BC = AC

What is the correct reason for statement #2?

Addition POE

Substitution
E                F
A               B                                        C
Def. of congruent segments
Segment Addition

1.  Given

2.  __?__

3.  __?__

1.  AB = EF

2.  AB + BC = AC

3.  EF + BC = AC

What is the correct reason for statement #3?

Addition POE

Substitution
E                F
A               B                                        C
Def. of congruent segments
Segment Addition

1.  Given

2.  __?__

3.  __?__

What is the correct reason for statement  #1

Given

Def. of straight angle

1.  ∡PRT is a straight angle

2.  m∡PRT = 180

3.  m∡PRT = m∡PRQ + m∡QRT

4.  180 = m∡PRQ + m∡QRT

∙P
∙Q
∙R
Angle Addition
Assumed from diagram
∙T

1.  __?__

2.  __?__

3.  __?__

4.  __?__

What is the correct reason for statement  #2

Given

Def. of straight angle

1.  ∡PRT is a straight angle

2.  m∡PRT = 180

3.  m∡PRT = m∡PRQ + m∡QRT

4.  180 = m∡PRQ + m∡QRT

∙P
∙Q
∙R
Angle Addition
Assumed from diagram
∙T

1.  __?__

2.  __?__

3.  __?__

4.  __?__

What is the correct reason for statement  #3

Given

Def. of straight angle

1.  ∡PRT is a straight angle

2.  m∡PRT = 180

3.  m∡PRT = m∡PRQ + m∡QRT

4.  180 = m∡PRQ + m∡QRT

∙P
∙Q
∙R
Angle Addition
Assumed from diagram
∙T

1.  __?__

2.  __?__

3.  __?__

4.  __?__

What is the correct reason for statement  #4

Substitution

Def. of straight angle

1.  ∡PRT is a straight angle

2.  m∡PRT = 180

3.  m∡PRT = m∡PRQ + m∡QRT

4.  180 = m∡PRQ + m∡QRT

∙P
∙Q
∙R
Angle Addition

Straight ∡'s are congruent

∙T

1.  __?__

2.  __?__

3.  __?__

4.  __?__

1.  VW ≅ WX

2.  WX ≅ XY

3.  VW ≅ XY

Def. of ≅ segments

What is the correct reason for statement #3?

 Transitive

V                    W                  X                    Y
Substitution
Segment Addition

1.  Given

2.  Given

3.  __?__

Def. of congruent angles

1.  ∡LQM is a right angle

2.  m∡LQM = 90

3.  m∡MQW = 90

4.  ∡LQM ≅ ∡MQW

Def. of right angle
What is the correct reason for Statement #2?
∙L
∙M
∙Q

Angle  Addition

Rt. angles are ≅

∙W

1.  Given

2. __?__

3.  Given

4.  __?__

Def. of congruent angles

1.  ∡LQM is a right angle

2.  m∡LQM = 90

3.  m∡MQW = 90

4.  ∡LQM ≅ ∡MQW

Def. of right angle
What is the correct reason for Statement #4?
∙L
∙M
∙Q

Angle  Addition

Rt. angles are ≅

∙W

1.  Given

2. __?__

3.  Given

4.  __?__

Def. of  congruent ∡'s
Transitive

What is the correct reason for Statement #3

1.  ∡HED ≅ ∡DEF

2.  ∡DEF ≅ ∡FEG

3.  ∡HED ≅ ∡FEG

 E
H
     D
F
Def. of angle trisector
Substitution
G

1.  Given

2.  Given

3.  __?__

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