Geometry Notes G.6 Triangle Basics, Congruence                                     Mrs. Grieser 
         Name: __________________________________________  Date: _______________ Block: ________   
         Triangle Basics 
            Definition:  A triangle is a polygon with ______ sides.   
            A triangle with 3 ________ A, B, and C is written as ∆ABC. 
         Classify Triangles by Sides: 
         Scalene:  No sides                      Isosceles:  At least 2 sides            Equilateral:  3 sides 
                                                                                                                    
         Classify Triangles by Angles: 
         Acute:  3 acute               Right:  1 right             Obtuse: 1 obtuse angle  Equiangular: 3 
         angles                        angle                                                        angles 
                                                                                          
                                                                                                                          
            Interior angles are those angles on the inside of a triangle.   
             Name interior angles: _______________________ 
            Exterior angles are formed when the lines of the triangle are 
             extended.  Name exterior angles:_____________________  
                                      Triangle Sum Theorem 
           The sum of the measures of the interior angles of a triangle is 
               o
          180 . 
             
            A corollary to a theorem is a statement that can be proved easily using the theorem.  
                          Corollary to the Triangle Sum Theorem 
          The acute angles of a right triangle are complementary. 
          
                                     Exterior Angle Theorem 
          The measure of an exterior angle of a triangle is equal to the sum 
          of the measures of the two nonadjacent interior angles. 
         Examples: 
         a)  Find x; classify the      b)  Find x; classify the     c)  Find mB, m1                d)  Find the measures 
             ∆                             ∆                                                             of the numbered 
                                                                                                         s 
                        
                                                                                                      
                                                                      
                                                            Geometry Notes G.6 Triangle Basics, Congruence                       Mrs. Grieser  Page 2 
                                                            Triangle Congruence 
                                                                                          In two congruent figures, all the 
                                                                                           corresponding parts are congruent 
                                                                                           (Corresponding Parts of Congruent Triangles 
                                                                                           are Congruent: CPCTC). 
                                                                                          In polygons, this means corresponding sides 
                                                                                           and angles are congruent. 
                                                                                          When writing congruence statements, always 
                                                                                           list the congruent parts in the same order.  
                                                                                                                                                                                                                                                                        Third Angles Theorem 
                                                                                    If two angles of one triangle are congruent to two angles of 
                                                                                    another triangle, then the third angles are also congruent. 
                                                                                                                                                Properties of Congruent Triangles Theorem 
                                                                                                        Reflexive Property of Congruent Triangles 
                                                                                                         o  For any ∆ ABC, ∆ABC ∆ABC 
                                                                                                        Symmetric Property of Congruent Triangles 
                                                                                                         o  If ∆ABC ∆DEF, then ∆DEF ∆ABC 
                                                                                                        Transitive Property of Congruent Triangles 
                                                                                                         o  If ∆ABC ∆DEF and ∆DEF ∆JKL, then ∆ABC∆JKL 
                                                            Examples: 
                                                            a)  Identify parts:                                                                                                                                                                                                                                                                                               b)  ∆ABC∆DEF                                                                                                                                                                                                                                                                                                     c)  Find x.  
                                                                angles:                                                                                                                                                                                                                                                                                                            Find x and y. 
                                                             
                                                             
                                                               sides: 
                                                             
                                                            conclusion: 
                                                            ___________ 
                                                            d) Find x.                                                                                                                                                                                                                                                                                                         e) Given the figure at right, prove ACDCAB 
                                                                                                                                                                                                                                                                                                                                                                                        Statements                                                                                                                                                                                           Reasons 
                                                                                                                                                                                                                                                                                                                                                                                        1)  ADCB,DC BA  1)Given 
                                                                                                                                                                                                                                                                                                                                                                                        2)  AC AC                                                                                                                                                                                           2) ____________________ 
                                                                                                                                                                                                                                                                                                                                                                                        3)  ACDCAB;                                                                                                                                                                                       3) Given 
                                                                                                                                                                                                                                                                                                                                                                                                                       CADACB                                                                                                                                                                                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                                                                                                                                                                        4)  BD                                                                                                                                                                                            4) ____________________ 
                                                                                                                                                                                                                                                                                                                                                                                        5) ACDCAB                                                                                                                                                                                         5) Def. of   figures 
                                                            You Try...                                                                                                                                                                                                                                                                                                          
                                                            a)  In the diagram,                                                                                                                                                                                                                                                                                                                                                                                                                                                         b)  FGHKSTUV.  
                                                                                             QRSTWXYZ.  Find the                                                                                                                                                                                                                                                                                                                                                                                                                                                     Find the value of x 
                                                                                           value of x and y.                                                                                                                                                                                                                                                                                                                                                                                                                                                          and mG.