Page 130 - Math Course 3 (Book 2)
P. 130

Proportional Parts of Triangles
          Mo. 10


           Lesson 4                                         COROLLARIES



                                                            10.1 If three or more parallel lines intersect two
                                                                 transversals, then they cut off the transver-
          KEY CONCEPTS:
                                                                 sals proportionally.
          1. Use proportional parts of triangles.                                        AB     DE
                                                                       ↔ ↔ ↔
          2. Divide a segment into parts.                   Example: If DA || EB || FC, then   =
                                                                                         BC     EF
                                                                      AB  =   DE  and  AC   =   DF
                                                                      BC      EF       BC       EF

          MO. 10 - L4a                                      7.2  If three ore more parallel lines cut off
                                                                 congruent segments on one transversal,
             Using Proportional Parts of                         then they cut off congruent segments on
                                                                 every transversal.
                          Triangles

                                                            Example: If AB ≅ BC, then DE ≅  EF.
         THEOREM 10.4                                                                      F


         Triangle Proportionality Theorem                                           E

         If a line is parallel to one side of a triangle and              D
         intersects the other two sides in two distinct
         points, then it separates these sides into segments
         of proportional lengths.
                            BA       DE                                   A
         Example: If BD || AE,   =
                            CB       CD
                                                                                    B
                                  C
                                                                                           C



                        B               D
                                                                         Let’s Begin



                   A                  E
                                                           Find the Length of a Side
         THEOREM 10.5                                         Example


         Converse of the Triangle Proportional

         If a line intersects two sides of a triangle and    In △RST, RT || VU, SV = 3, VR = 8, and UT = 12.
         separates the sides into corresponding segments    Find SU.
         of proportional lengths, then the line is parallel to
         the third side.                                                R           8       V   3

         Example:   BA  =  DE  , then BD || AE.                                                        S
                   CB      CD
                                                                                                x
                           C
                                                                                          U



                        B              D
                                                                            12
                                          E
                        A                                    T
    122
   125   126   127   128   129   130   131   132   133   134   135