Geometry Notes 3.1 - Congruent Triangles by cometjunkie43

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									Geometry Notes 3.1 – Congruent Triangles
1. Congruent Triangles

        Reminder: the word “Congruent” means


        Def’n: Two triangles are congruent when




        Ex) Name and mark the corresponding congruent parts if ∆ABC ≅ ∆XYZ .
           B




                                         Y
                                 C
A




                     Z                            X



        Ex) Name the corresponding congruent parts if ∆ABC ≅ ∆ADE .


    B                                        D



                         A
                     1       2

            C                        E



        Ex) Name the corresponding congruent parts (without a diagram) if ∆PQR ≅ ∆TWV .




30 Notes 3.1, Page 1 of 5
L. Morvan, Cypress College
2. SSS Method for proving congruent triangles

    SSS:




    Ex) Write the proof.                                                          A

           Given:    AD ≅ AB
                     C is the midpoint of DB

           Prove: ∆ADC ≅ ∆ABC
                                                              D                                   B
                                                                                      C

             Statements (specific)                                Reasons (general)



1. ____________________________                1. ___________________________________________

2. ____________________________                2. ___________________________________________

3. ____________________________                3. ___________________________________________

4. ____________________________                4. ___________________________________________



    Ex) Write the proof.                                          X                       Y

           Given:    XW ≅ YZ , XZ ≅ YW

           Prove: ∆XZW ≅ ∆YWZ
                                                          W                                   Z
             Statements (specific)                                Reasons (general)


1. ____________________________                1. ___________________________________________

2. ____________________________                2. ___________________________________________

3. ____________________________                3. ___________________________________________

(hint: try drawing the triangles separately)




30 Notes 3.1, Page 2 of 5
L. Morvan, Cypress College
3. SAS Method for proving congruent triangles

   SAS:




   Ex) Write the proof.                                                                 D
                                                                B

          Given:   BE and AD bisect each other                          C
                                                                    1       2
          Prove: ∆ABC ≅ ∆DEC
                                                   A
                                                                                    E
            Statements (specific)                          Reasons (general)


1. ____________________________         1. ___________________________________________


2. ____________________________         2. ___________________________________________

3. ____________________________         3. ___________________________________________

4. ____________________________         4. ___________________________________________


                                                                            A
   Ex) Write the proof.

          Given:   AD ≅ AB
                   AC bisects ∠DAB
                                                       D                                    B
                                                                                C
          Prove: ∆ADC ≅ ∆ABC

            Statements (specific)                          Reasons (general)



1. ____________________________         1. ___________________________________________

2. ____________________________         2. ___________________________________________

3. ____________________________         3. ___________________________________________

4. ____________________________         4. ___________________________________________



30 Notes 3.1, Page 3 of 5
L. Morvan, Cypress College
4. ASA Method for proving congruent triangles

   ASA:




   Ex) Write the proof.                                                            D
                                                             B
          Given: ∠A ≅ ∠D                                             C
                 BE bisects AD                                   1       2

          Prove: ∆ABC ≅ ∆DEC                    A
                                                                               E

            Statements (specific)                       Reasons (general)



1. ____________________________     1. ___________________________________________

2. ____________________________     2. ___________________________________________

3. ____________________________     3. ___________________________________________

4. ____________________________     4. ___________________________________________


   Ex) Write the proof.                                                   Q
                                                    P                              R
                                                                         1 2
          Given: QT bisects ∠PTR
                   QT ⊥ PR
                                                                      3 4
          Prove: ∆PQT ≅ ∆RQT                                              T

            Statements (specific)                       Reasons (general)



1. ____________________________     1. ___________________________________________

2. ____________________________     2. ___________________________________________

3. ____________________________     3. ___________________________________________

4. ____________________________     4. ___________________________________________

5. ____________________________     5. ___________________________________________

30 Notes 3.1, Page 4 of 5
L. Morvan, Cypress College
5. AAS Method for proving congruent triangles

    AAS:




                                                      E                                     G
    Ex) Write the proof.

           Given: ∠E ≅ ∠G                                                   F
                     ∠EDH ≅ ∠GHD
                                                           D                         H
           Prove: ∆EDH ≅ ∆GHD


             Statements (specific)                             Reasons (general)



1. ____________________________                1. ___________________________________________

2. ____________________________                2. ___________________________________________

3. ____________________________                3. ___________________________________________


(hint: try drawing the triangles separately)




30 Notes 3.1, Page 5 of 5
L. Morvan, Cypress College

								
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