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PROVING TRIANGLES CONGRUENT

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  • pg 1
									PROVING TRIANGLES
   CONGRUENT
FOUR WAYS TO PROVE
TRIANGLES ARE CONGRUENT
   Side-Side-Side Postulate (SSS)

   Side-Angle-Side Postulate (SAS)

   Angle-Side-Angle Postulate (ASA)

   Angle-Angle-Side Theorem (AAS)
    Side-Side-Side (SSS)
                If the sides of a triangle are
                  congruent to the sides of a
                second triangle, then the two
    O              triangles are congruent.

                         Since the following information is true:
                   A
                               BO  MA; OY  AN ; BY  MN
            Y
B                           Then the two triangle must be congruent.

                                      BOY  MAN
        M               N
    Side-Angle-Side (SAS)
            If two sides and the included
              angle are congruent to two
            sides and the included angle of
    O       another triangle, then the two
                triangles are congruent.
                A

            Y
B
                         WHAT IS AN INCLUDED ANGLE?


        M            N
    Included Angles
           An included angle is the angle formed
            at the intersection of two sides of a
            triangle
    O                       So, the included angle
                            between BO and BY would
                    A       be angle B.

                Y           The included angle
B                           between MA and MN
                            would be angle M.
            M           N
Are these two triangles
congruent?
        O                   A




              Y     M            N
B


       If angle B is congruent to
        angle M, then the two
        triangles are congruent
        because of SAS.
    Angle-Side-Angle (ASA)
       If two angles and the included side
         of a triangle are congruent to two
           angles and the included side of
           another triangle, then the two
               triangles are congruent.
         O                             A

                    WHAT IS AN
                    INCLUDED
                      SIDE?
              Y                  M            N
B
    Included Sides
       An included side between two angles is
        the side that is adjacent to both angles.



        O          So, BY is the included side
                   between angle B and angle Y


              Y
B
So are these two triangles
congruent?
        O                   A




             Y       M          N
B

       Yes, because two angles
        and the included side are
        congruent which makes
        the two triangles
        congruent by ASA.
        Angle-Angle-Side (AAS)
       If two angles and a nonincluded side
            of a triangle are congruent are
            congruent to two angles and a
        nonincluded side of another triangle,
        then the two triangles are congruent.
          O                 A




               Y
B                    M          N
Are these two triangles
congruent?
        O               A




             Y
 B                M         N

    Since OY is not included
     between B and Y and AN is
     not included between M and
     N, these two triangles are
     congruent because of AAS.
Angle-Side-Side
   THERE IS NO SUCH THING AS
    ANGLE SIDE SIDE BECAUSE
    YOU CAN’T USE THAT KIND OF
    LANGUAGE AT SCHOOL.
Angle-Angle-Angle
   This cannot prove two triangles
    congruent. It just shows that they are
    similar.
                   If both of these

                    triangles are
                    equiangular, they have
                    three congruent
                    angles. Are they
                    congruent triangles?

								
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