Page 131 - Math Course 3 (Book 2)
P. 131

Proportional Parts of Triangles




                Form the Triangle Proportionality Theorem,        Proportional Segments
                  SV       SU
                  VR   =   UT                                        Example
                Substitute the known measures.


                      3  =   X                                     MAPS
                      8     12                                     In the figure, Larch, Maple, and Nuthatch Streets
                                                                   are all parallel. The figure shows the distances in
                       3(12) = 8x  Cross products                  city blocks that the streets are apart. Find x.


                            36 = 8x  Multiply.
                     36  = x   Divide each side by 8.                               26          13
                     8
                     1                                                                            16
                 4       = x   Simplify.
                     2                                                        Larch  x

                                               1                                                      Nuthatch
                   Answer                  4                                                  Maple
                                               2


                                                                   Notice that the streets form a triangle that is cut by
               Determine Parallel Lines                            parallel lines. So you can use the Triangle
                                                                   Proportionality Theorem.
                   Example                                          26      X


                                                                    13   =  16   Triangle Proportionality Theorem
                                                 1
                In △DEF, DH = 18, HE = 36, and DG =       GF.      26(16) = 13x  Cross products
                                                 2

                Determine whether GH || FE. Explain.
                                                                        416 = 13x  Multiply.

                                                                           32 = x  Divide each side by 13.
                                D



                                                                      Answer                   32

                           G                    H



                           F                         E


                 In order to show that GH || FE, we must show that
                   DG   =  DH  DG =   1  GF, so  DG  =  1
                   GF      HE        2          GF      2

                         DG      1        DH      18      1
                  Since       =     and       =       or
                         GF      2        HE      36      2
                  the sides have proportional length


                                                since the segments have
                                    DH
                               DG
                   Answer         =
                                    HE
                               GF             proportional lengths,
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