Answer:
The correct options are;
1. Definition of supplementary angles
2. m∠1 + m∠2 = m∠1 + m∠3
3. m∠2 = m∠3 
4. Definition of Congruent Angles
Step-by-step explanation:
The two column proof is presented as follows;
Statement            Reason
                                  Reason
1. ∠1 and ∠2 are supplementary     Given
     Given
   ∠1 and ∠3 are supplementary
 ∠1 and ∠3 are supplementary
2. m∠1 + m∠2 = 180°         Definition of supplementary angles
                    Definition of supplementary angles
  m∠1 + m∠3 = 180°
   m∠1 + m∠3 = 180° 
3. m∠1 + m∠2 = m∠1 + m∠3       Transitive Property
          Transitive Property 
4. m∠2 = m∠3        Subtraction Property of Equality
                               Subtraction Property of Equality
5. ∠2 ≅ ∠3        Definition of Congruent Angles
                                    Definition of Congruent Angles
Given that angles ∠1 and ∠2 are supplementary angles and angles ∠1 and ∠3 are are also supplementary angles, then the sums of m∠1 + m∠2 and m∠1 + m∠3 are equal, therefore, ∠2 and ∠3 have equal quantitative value and therefore ∠2 = ∠3 and by definition, ∠2 ≅ ∠3.
 
        
             
        
        
        
Answer:
STUV is a square
Step-by-step explanation:
segment length² = (x-x₁)² + (y-y₁)²
ST²: (-9 - 1)2 + (14 - 10)² = (-10)² + 4² = 116   (the rest follow this formula)
TU² = 116    TV² = 232    SU² = 232   SV² = 116   UV² = 116
ST = TU =SV = UV  (4 sides congruent)
TV = SU  (diagonal equal)
This is a square
 
        
             
        
        
        
The answer is b because it is b
 
        
                    
             
        
        
        
Answer:
a and b.
Step-by-step explanation:
I’ll explain by giving an example.
Let’s say that: a=3;b=4;c=5; => they all are consecutive -> their sum is 12.
=> if we use a) n=3 => 3*n+3=3*3+3=12 => correct.
b) n+(n+1)+(n+2)= 3+4+5=12=> correct.
c)n+2n+3n=3+6+9=18=>incorrect.
d)3n=3*3=9=>incorrect.