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Congruence


 Congruent
The Conditions
 Congruent Triangles

                         Click what you want
                                to learn
Congruent


a) The all sides of
   corresponding sides are
   equal                     The Conditions for
b) The angles of             Similarity of
   Corresponding sides       Two Plane Figures are:
   are equal
c) The shapes of both
   figure are same
Congruent Triangle

                                  The example:
         A            D           a) The Corresponding sides
a)
                                     (look the same sign) are:
     C       B    F       E          AC with DF, AB with
     R           U            V      DE, and BC with EF
b)
                                  b) Equal angle of
     S            T                  Corresponding side:
                              W      <R with <W, <S with
c)
                                     <V, and <T with <U
                                  c) Both of Plane Figures are
                                     Triangle
Congruent Triangles


                                To Prove that 2 Triangles are
                                Congruent:
A               6cm             a) Side, Side, Side
            T             U
                                The all sides are in equal
          7cm       7cm   5cm
    5cm

                B         S
C     6cm
Congruent Triangles


                                 To Prove that 2 Triangles are
                                 Congruent:
A                      6cm
                             U   b) Two Sides, One Angle
          T      45              The angle coincided by two
      7cm             7cm            sides (AB and BC or UT
                                     and TS)
            45    B
    6cm
                             S
C
Congruent Triangles

A                           6cm                To Prove that 2 Triangles are
                   T   45          90
                                           U
                                               Congruent:
                                               c) Two Angles, One Side
              45
                                                1. The angles known on the
90                 B                       S
C       6cm                                        side
    A                  6cm                      2.The side face to one of two
               T              90       U
    55                                             angles

                                  55
    90 6cm         B                   S
    C
Example

Answer:
We prove it based on the
condition, that we have learn
before. We look for the same
                                           C
                                                           B
sign:                                          E
 <CAE equal to <EBD
 CE equal to ED                  A
 <CEA equal to <BED (It hasnt                    D
sign, but its vertical angles
                                  Prove that ACE and      BDE
The Conclusion: ACE                      are congruent
and BDE are congruent
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Mathematics - Congruent

  • 1. Congruence Congruent The Conditions Congruent Triangles Click what you want to learn
  • 2. Congruent a) The all sides of corresponding sides are equal The Conditions for b) The angles of Similarity of Corresponding sides Two Plane Figures are: are equal c) The shapes of both figure are same
  • 3. Congruent Triangle The example: A D a) The Corresponding sides a) (look the same sign) are: C B F E AC with DF, AB with R U V DE, and BC with EF b) b) Equal angle of S T Corresponding side: W <R with <W, <S with c) <V, and <T with <U c) Both of Plane Figures are Triangle
  • 4. Congruent Triangles To Prove that 2 Triangles are Congruent: A 6cm a) Side, Side, Side T U The all sides are in equal 7cm 7cm 5cm 5cm B S C 6cm
  • 5. Congruent Triangles To Prove that 2 Triangles are Congruent: A 6cm U b) Two Sides, One Angle T 45 The angle coincided by two 7cm 7cm sides (AB and BC or UT and TS) 45 B 6cm S C
  • 6. Congruent Triangles A 6cm To Prove that 2 Triangles are T 45 90 U Congruent: c) Two Angles, One Side 45 1. The angles known on the 90 B S C 6cm side A 6cm 2.The side face to one of two T 90 U 55 angles 55 90 6cm B S C
  • 7. Example Answer: We prove it based on the condition, that we have learn before. We look for the same C B sign: E <CAE equal to <EBD CE equal to ED A <CEA equal to <BED (It hasnt D sign, but its vertical angles Prove that ACE and BDE The Conclusion: ACE are congruent and BDE are congruent