Page 139 - Math Course 3 (Book 2)
P. 139

Proportional Relationships of Similar Triangles






                                            JK    JL               MO. 10 - L5b
                   Substitute in the equation                      to get
                                               =
                                            QR    QS
                    JK
                                                    2JM
                          2JM
                                              JK
                                         . Simplify to find                        ,    Special Segments of Similar
                        =
                                                 =
                    QR    2QT                QR     2QT                            Triangles
                   Therefore, △JKM ~△QRT by SSS Similarity.
                Your Turn!                                         THEOREMS
                                                                   Special Segments of Similar Triangles
               Perimeters of Similar Triangles
                                                                   10.8  If two triangles are similar, then the mea-
                If △PNO ~ △XQR, PN = 6, XQ = 20, QR = 20√2,              sures of the corresponding altitudes are
                and RX = 20, find the perimeter of △PNO.                 proportional to the measures of the
                                                                         corresponding sides.
                                    Q
                                                                         Abbreviation: ~△s have corr. altitudes
                                                                         proportional to the corr. sides.
                                                                                                          U
                 N                  20
                                                                               Q
                                                        20√2
                 6
                                                                                                   T      W   V
                 P           O      X           20          R
                                                                   P           A       R
                 A. 18√2                                               QA      PR      QR     PQ
                                                                           =       =       =
                 B. 6√2                                                UW      TV      UV     TU
                 C. 12 + 6√2
                 D. 72√2
                                                                   10.9  If two triangles are similar, then the mea-
                                                                         sures of the corresponding angle bisectors
                   Answer                                                of the triangle are proportional to the mea-
                                                                         sures of the corresponding sides.

               Write a Proof                                             Abbreviation: ~△s have corr. ∠bisectors
                                       5                                 proportional to the corr. sides.
                △EFG ~ △MSY and EF =        MS. Find the ratio of
                                       4
                the length of a median of △EFG to the length of a                                           U
                median of △MSY.                                                  Q


                 A.  4
                    5                                                                              T    X     V

                    1                                              P           B       R
                 B.
                    4
                                                                       QB      PR      QR     PQ
                                                                           =       =       =
                    1                                                  UX      TV      UV     TU
                 C.
                    5

                 D.  5
                    4




                   Answer

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