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Ch4.2_CongruentTriangles.notebook   October 24, 2011




             Chapter 4.2
             Congruent Triangles




                                                       1
Ch4.2_CongruentTriangles.notebook                     October 24, 2011




          Congruent means same measure (or size and shape)


                                    ≅
     Congruent triangles have
     congruent angles and
     congruent sides B
     X


         Y                          Z
                                        A       C




                                                                         2
Ch4.2_CongruentTriangles.notebook                  October 24, 2011




        Types of Triangle Congruences
                 The SSS Postulate
                       (side­side­side)
           2 triangles are congruent if:
           3 sides of one triangle are equal to 
           the 3 sides of the other triangle




                                                                      3
Ch4.2_CongruentTriangles.notebook                October 24, 2011




        Types of Triangle Congruences
                 The SAS Postulate
                   (side­angle­side)
          2 triangles are congruent if:
          2 sides and their included angle of one 
          triangle are equal to 2 sides and their 
          included angle of the other triangle

                                Included angle




                                                                    4
Ch4.2_CongruentTriangles.notebook               October 24, 2011




        Types of Triangle Congruences
                 The ASA Postulate
                   (angle­side­angle)
          2 triangles are congruent if:
          2 angles and their included side of one 
          triangle are equal to 2 angles and their 
          included side of the other triangle

                                Included side




                                                                   5
Ch4.2_CongruentTriangles.notebook                          October 24, 2011


                  Are the following triangles congruent?
                  If so, by what congruence postulate?




                                                                              6
Ch4.2_CongruentTriangles.notebook   October 24, 2011




        Which Postulate?




                                                       7
Ch4.2_CongruentTriangles.notebook                October 24, 2011




                                    Prove: ΔVWX ≅ ΔZXY



             Statement                  Reason




                                     Definition of
                                     perpendicular
                                     lines




                                                                    8
Ch4.2_CongruentTriangles.notebook                October 24, 2011


     Given: RQ = RS                         R
            RT bisects <QRS

     Prove:  ΔQRT = ΔSRT

                                            T
                                    Q                  S

             Statement                  Reason




                                                                    9
Ch4.2_CongruentTriangles.notebook   October 24, 2011




                    Page 156
                     # 1­7




                                                       10

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Ch4.2 Congruent Triangles

  • 1. Ch4.2_CongruentTriangles.notebook October 24, 2011 Chapter 4.2 Congruent Triangles 1
  • 2. Ch4.2_CongruentTriangles.notebook October 24, 2011 Congruent means same measure (or size and shape) ≅ Congruent triangles have congruent angles and congruent sides B X Y Z A C 2
  • 3. Ch4.2_CongruentTriangles.notebook October 24, 2011 Types of Triangle Congruences The SSS Postulate (side­side­side) 2 triangles are congruent if: 3 sides of one triangle are equal to  the 3 sides of the other triangle 3
  • 4. Ch4.2_CongruentTriangles.notebook October 24, 2011 Types of Triangle Congruences The SAS Postulate (side­angle­side) 2 triangles are congruent if: 2 sides and their included angle of one  triangle are equal to 2 sides and their  included angle of the other triangle Included angle 4
  • 5. Ch4.2_CongruentTriangles.notebook October 24, 2011 Types of Triangle Congruences The ASA Postulate (angle­side­angle) 2 triangles are congruent if: 2 angles and their included side of one  triangle are equal to 2 angles and their  included side of the other triangle Included side 5
  • 6. Ch4.2_CongruentTriangles.notebook October 24, 2011 Are the following triangles congruent? If so, by what congruence postulate? 6
  • 7. Ch4.2_CongruentTriangles.notebook October 24, 2011 Which Postulate? 7
  • 8. Ch4.2_CongruentTriangles.notebook October 24, 2011 Prove: ΔVWX ≅ ΔZXY Statement Reason Definition of perpendicular lines 8
  • 9. Ch4.2_CongruentTriangles.notebook October 24, 2011 Given: RQ = RS R RT bisects <QRS Prove:  ΔQRT = ΔSRT T Q S Statement Reason 9
  • 10. Ch4.2_CongruentTriangles.notebook October 24, 2011 Page 156 # 1­7 10