Geometry 4-5 More Congruent Triangles by cometjunkie43

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									Geometry 4-5 More Congruent Triangles

A. Current Congruences
   1. We know three ways to prove triangles congruent so far. They are ________________,
      ______________, and _______________.

B. Postulate 4-3 ASA Postulate ( _________-_________-__________ Postulate)
   -If two angles and the __________ side of one triangle are congruent to two angles and the
   ___________ side of another triangle, then the triangles are _____________.
                                                                             C
   Ex. 1:                                        A
   Given:     BE bisects AD.                                             2
                                                                 1
              <A≅<D                                                  E
   Prove:     AB ≅ DC                                                             D
                                                     B

   Statements                                            Reasons
   1.) BE bisects AD                                     1.)
       <A≅<D
   2.)                                                   2.) Vertical <’s are ≅
   3.) AE ≅ ED                                           3.)
   4.) ∆ AEB ≅ ∆DEC                                      4.)
   5.) AB ≅ DC                                           5.)

C. Theorem 4-5 AAS Postulate ( _________-__________-________ Postulate)
   -If two angles and a_____________ side of one triangle are congruent to the corresponding
   two angles and a_____________ side of a second triangle, then the two triangles are
   ___________.
                                   S                         T                                    T
                                                                     S
   Ex. 2: Write a proof

   Given:     < PSU ≅ < PTR            R                 U                            U   R
              SU ≅ TR
   Prove:     SP ≅ TP
                                             P                               P                P

   Statements                                            Reasons
   1.) < PSU ≅ < PTR                                     1.)
       SU ≅ TR
   2.)                                                   2.) Reflexive
   3.)                                                   3.)
   4.) SP ≅ TP                                           4.)
Ex. 3: Some of the measurements of ∆ ABC and ∆ DEF are given. Can you determine if the
two triangles are congruent?
                          C                                F

                                    2.5                              2.5

                    40°                              40°
                A                         B      D                               E
                              4.0                              4.0


Explore: Since we know < A ≅ < D, and we know AB ≅ DE, and CB ≅ FE ; we know that
there are two congruent sides and one non-included angle that are congruent. Our five
methods of proving triangles are:

1.)   definition of congruent ∆’s (all 3 sides and all 3 angles)
2.)   SSS congruence
3.)   SAS congruence
4.)   ASA congruence
5.)   AAS congruence

-     since none of these work, the triangles must not be congruent.

Counter Example: here is a case where the triangles are obviously not congruent, but the
same conditions hold true.


                                                                           Y

                          C                                          W               2.5
                                    2.5

                    40°                                        40°
                A                         B                X                               Z
                              4.0                                          4.0


HW: Geometry 4-5 p. 211-213
9-11 all, 15-16 (two column), 23-28 all, 31-33 all, 35-41 all

								
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