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Proving Triangles Congruent - World of Teaching

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					Proving Triangles
   Congruent
The Idea of a Congruence

Two geometric figures with
exactly the same size and
shape.
                      F


       B



       A     C    E   D
How much do you
   need to know. . .

   . . . about two triangles
         to prove that they
         are congruent?
        Corresponding Parts
In Lesson 4.2, you learned that if all
  six pairs of corresponding parts (sides
  and angles) are congruent, then the
  triangles are congruent.
    1. AB  DE
    2. BC  EF
    3. AC  DF
    4.  A   D
                            ABC   DEF
    5.  B   E
    6.  C   F
Do you need all six ?

          NO !

                   SSS
                   SAS
                   ASA
                   AAS
   Side-Side-Side (SSS)




1. AB  DE
2. BC  EF    ABC   DEF
3. AC  DF
  Side-Angle-Side (SAS)




1. AB  DE
2. A   D    ABC   DEF
3. AC  DF
              included
                angle
      Included Angle
The angle between two sides




 G          I           H
        Included Angle

           Name the included angle:
    E

           YE and ES     E
           ES and YS     S

Y   S      YS and YE     Y
  Angle-Side-Angle (ASA)




1. A   D
2. AB  DE     ABC   DEF
3.  B   E
               include
                   d
                 side
      Included Side
The side between two angles




 GI          HI               GH
        Included Side

          Name the included angle:
    E

          Y and E   YE
          E and S   ES
Y   S     S and Y   SY
  Angle-Angle-Side (AAS)




1. A   D
2.  B   E   ABC   DEF
3. BC  EF
               Non-included
                   side
Warning: No SSA Postulate

          There is no such
          thing as an SSA
             postulate!



      B               E

                             F
      A      C
                      D

          NOT CONGRUENT
Warning: No AAA Postulate
         There is no such
         thing as an AAA
            postulate!



                E
   B



   A     C                  F
                D

        NOT CONGRUENT
The Congruence Postulates
       SSS correspondence

       ASA correspondence

       SAS correspondence

       AAS   correspondence
       SSA correspondence

       AAA correspondence
Name That Postulate
               (when possible)




SAS
                   ASA




 SSA                 SSS
 Name That Postulate
                (when possible)




AAA
                       ASA



   SAS                     SSA
        Name That Postulate
                       (when possible)




                                   Vertical
                                   Angles
Reflexive
Property    SAS                    SAS




        Vertical           Reflexive
        Angles     SAS     Property    SSA
HW: Name That Postulate
                  (when possible)
HW: Name That Postulate
                  (when possible)
             Let’s Practice
 Indicate the additional information needed
 to enable us to apply the specified
 congruence postulate.

For ASA:   B  D
For SAS:   AC  FE
For AAS:   A  F
                    HW
 Indicate the additional information needed
 to enable us to apply the specified
 congruence postulate.

For ASA:

For SAS:

For AAS:
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posted:7/2/2012
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