Congruent Triangle Proofs 
           Complete each proof.                                                           
                          ̅̅̅̅           ̅̅̅̅
           1.  Given:     bisects   ,        , and             
            
                Prove:          
            
                  Statements                                                                 Reasons 
                                                                                              
                                                                                              
                                                                                              
                                                                                              
            
            
                          ̅̅̅̅    ̅̅̅̅                             ̅̅̅̅
           2.  Given:         , G is the midpoint of    
                          ̅̅̅̅    ̅̅̅̅
                Prove:          
            
                  Statements                                                                 Reasons 
                                                                                              
                                                                                              
                                                                                              
                                                                                              
                                                                                              
                                                                                              
                         ̅̅̅̅     ̅̅̅̅ ̅̅̅̅
           3.  Given:        ,    bisects      
            
                Prove:              
            
            
                  Statements                                                                 Reasons 
                                                                                              
                                                                                              
                                                                                              
                                                                                              
                                                     
                                      ̅                                                                                             ̅̅̅̅̅
               4.  Given:     is an altitude of      and L is the midpoint of    
                
                       Prove:              
                
                         Statements                                                                                                   Reasons 
                                                                                                                                       
                                                                                                                                       
                                                                                                                                       
                                                                                                                                       
                                                                                                                                       
                                                                                                                                       
                                                                                                                                       
                
                                                                            
                                                                Congruent Triangle Proofs 
           Complete each proof.                                                           
                          ̅̅̅̅           ̅̅̅̅
           1.  Given:     bisects   ,        , and             
            
                Prove:          
            
                  Statements                                                                 Reasons 
                  ̅̅̅̅           ̅̅̅̅                                                        Given 
                     bisects   ,        , and             
                  ̅̅̅̅    ̅̅̅̅                                                               Definition of segment bisector 
                         
                                                                                             ASA 
                                                                                             Corresponding Parts of Congruent Triangles are 
                                                                                             Congruent 
            
                          ̅̅̅̅    ̅̅̅̅                             ̅̅̅̅
           2.  Given:         , G is the midpoint of    
                          ̅̅̅̅    ̅̅̅̅
                Prove:          
            
                  Statements                                                                 Reasons 
                  ̅̅̅̅    ̅̅̅̅                              ̅̅̅̅                             Given 
                       , G is the midpoint of    
                                                                                             Perpendicular lines form congruent right angles 
                  ̅̅̅̅    ̅̅̅̅                                                               Definition of midpoint 
                         
                  ̅̅̅̅    ̅̅̅̅                                                               Reflexive property 
                         
                                                                                             SAS 
                                                                                             Corresponding Parts of Congruent Triangles are 
                  ̅̅̅̅    ̅̅̅̅
                                                                                             Congruent 
                         ̅̅̅̅     ̅̅̅̅ ̅̅̅̅
           3.  Given:        ,    bisects      
            
                Prove:              
            
            
                  Statements                                                                 Reasons 
                  ̅̅̅̅    ̅̅̅̅ ̅̅̅̅                                                          Given 
                       ,    bisects      
                                                                                             Definition of angle bisector 
                  ̅̅̅̅    ̅̅̅̅                                                               Reflexive property 
                         
                                                                                             SAS 
                                      ̅                                                                                             ̅̅̅̅̅
               4.  Given:     is an altitude of      and L is the midpoint of    
                
                       Prove:              
                
                         Statements                                                                                                   Reasons 
                         ̅̅̅
                            is an altitude of      and L is the midpoint of                                                           Given 
                         ̅̅̅̅̅
                            
                         ̅̅̅       ̅̅̅̅̅                                                                                              Definition of altitude 
                                  
                                                                                                                                      Perpendicular lines form congruent right angles 
                         ̅̅̅̅̅        ̅̅̅̅                                                                                            Definition of midpoint 
                                
                         ̅̅̅       ̅̅̅                                                                                                Reflexive property 
                                  
                                                                                                                                      SAS 
                                                                                                                                      Corresponding Parts of Congruent Triangles are 
                                                                                                                                      Congruent