Three Ways to Prove Triangles Congruent - Randolph School by chchxinxin

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									Three Ways to Prove
Triangles Congruent

           Three
         Postulates
 Three Postulates
  Euclid stated these postulates as theorems.

If there exists a correspondence between the vertices
of two triangles such that three sides of one triangle
are congruent to the corresponding sides of the other
Triangle, the two triangles are congruent. SSS

SAS

ASA
            K

        1       2
                            KIT  KET ,
I   5               6   E

                            KI  KE , IT  ET , KT  KT
                             1   2, 3     4, 5    6
        3       4




            T
                A

                                    ABE  AIU ,
    U       1       2       E
                                    AB  AI , AE  AU , BE  IU
        3               4

                                     2  1, B  I , A  A
B
                                I
                T
                                  TGR  TEI ,
                                  TG  TE , TR  TI , GR  EI
        I   3       4 R            1    2,   4   3,   T T
                S
    1                     2

G                             E
                            IGE  REG,
                T



                            IG  RE , IE  RG, GE  GE
    I                   R
                                1   2,   4   3,   IGE  REG
            3       4

                S

        1               2
G                           E
Let’s look at some practice
problems
   http://regentsprep.org/Regents/math/c
    ongruen/Ltriangles.htm
   http://regentsprep.org/Regents/math/c
    ongruen/PracCong.htm

								
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