6.1A Congruent Triangles ANSWERS

					Geometry                                             6.1A Congruent Triangles                              Name __________________________
Completed:____ Correct:____ Grade:_______/10                                                                   Period____ Date_______________



  For questions 1-5, given the Triangle Congruent Postulate draw the corresponding markings.
  1. SSS               2. ASA             3. SAS              4. HL           5. AAS




  For questions 6-15, determine whether the following triangles can be proven congruent using the given information. If
  congruency can be proven, write a congruence statement and identify the postulate used to prove congruency. If
  not enough information is given, write not possible.
                    A
  6.                                                                         7.
                                                                                       A           B       S
                                    C           ΔABC  ΔSBT, by ASA                                                         ΔABC  ΔSBC, by SAS
            B




        S                   T
                                                                                                   C



  8.            A                       B                                    9.                                P
                                                     ΔABD  ΔCDB, by SSS                                                    NOT POSSIBLE
                                                                                   A
                                                                                                   C

       D                        C                                                                                  Q
                                                                                           B


                                                                                                   D
  10.                                            E                           11.
       A
                                                      ΔABC  ΔEDC, by AAS          A                           C           ΔABC  ΔADC, by HL
                            C

                                            D
                    B                                                                              B



  12.                   B                                                    13.
                                                                                       N

                                                ΔABD  ΔCBD, by SAS or SSS                                             A      ΔABC  ΔNMC, by AAS
                                                                                       M               C

            A                           C                                                                              B
                        D



  14.                   A                                                    15.
                                                                                               A                   B
           B                            D
                                                ΔABC  ΔADC, by SSS                                                        NOT POSSIBLE
                                                                                   D                       C

                        C
For questions 16-25, state one additional fact that would make the triangles congruent and name the postulate. Write
your answer as a conditional statement (IF, THEN).

16.                                                                       17.           G
                       B
       A                        If BC  DF, then ΔABC  ΔEDF by SAS                                                                            If LH  IK, then ΔGHL  ΔKJI by SAS
                                If C  F, then ΔABC  ΔEDF by AAS                                         L                                  If G  J, then ΔGHL  ΔKJI by ASA
                                                                                                                            K
                                If A  E, then ΔABC  ΔEDF by ASA             H           I                                                  If L  I, then ΔGHL  ΔKJI by AAS
          D            C        If AC  EF, then ΔABC  ΔEDF by HL
                        E
                                                                                                                J

           F




18.            Q                                                          19.
                                    If   MN  NP, then ΔMNQ  ΔPNO by HL                                                                If RS  UV, then ΔSRT  ΔVUW by ASA
                   P                If   QN  NO, then ΔMNQ  ΔPNO by HL                    R                       S           W       If ST  VW, then ΔSRT  ΔVUW AAS
                                    If   Q  O, then ΔMNQ  ΔPNO by AAS                                                               If RT  UW, then ΔSRT  ΔVUW AAS
                                    If   M  NPO, then ΔMNQ  ΔPNO by AAS
      M                         O
               N                                                                                                    U                   V
                                                                                                        T


20.        A           B                                                  21.
                                                                                    G               H           L               K
                                     If CB  DF, then ΔABC  ΔEFD by SSS                                                                 If   HI  KJ, then ΔGHI  ΔLKJ by HL
                       D
                                     If A  E, then ΔABC  ΔEFD by SAS                                                                 If   GH  LK, then ΔGHI  ΔLKJ by SAS
               C
                                                                                                                                         If   H  K, then ΔGHI  ΔLKJ by AAS
                                                                                                                                         If   I  J, then ΔGHI  ΔLKJ by ASA
                                F                                                   I                           J
                   E

22.                                                                       23.
               M                                                                    A               B           X                   Y
                                         If NO  PQ, then ΔMNO  ΔRPQ by SSS                                                                   If AB  XY, then ΔMNO  ΔRPQ by SSS
      N                     O            If M  R, then ΔMNO  ΔRPQ by SAS                                                                   If C  Z, then ΔMNO  ΔRPQ by SAS
      P                     Q
                                                                                                            C                           Z
                   R




                                                                                                                        F
24.                                                                       25.
       X               Y                                                                            E
                                         If XZ  WV, then ΔXYZ  ΔWUV by SAS                                            D               If EF  CB, then ΔEFD  ΔBCA by SSS
                                                                                                A
                                         If Y  U, then ΔXYZ  ΔWUV by ASA                                                            If A  D, then ΔEFD  ΔBCA by SAS
               Z                                                                                                    B
       W               U                 If X  W, then ΔXYZ  ΔWUV by AAS
                                                                                            C

               V


Identify the triangle congruence postulates given below.

26. If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are
congruent.          SAS

27. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are
congruent.           HL

28. If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are
congruent.          ASA

29. If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. SSS

30. If two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the
triangles are congruent.      AAS

				
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