Page 135 - Math Course 3 (Book 2)
P. 135

Proportional Parts of Triangles




                                                                  Congruent Segments
                To find y:

                                               8
                The segments with lengths 5y and       y + 7 are
                                               3
                congruent since parallel lines that cut off            4a – 5                     3b
                congruent segments on one transversal cut off
                congruent segments on every transversal.                                            5
                                                                       3a + 6                           b + 2
                                                                                                    3
                      8
                  5y =       y + 7  Equal lengths
                      3
                               Multiply each side by 3 to
                15y = 8y + 21
                               eliminate the denominator.
                                                                   Find a.
                 7y = 21       Subtract 8y from each side.            11
                                                                   A.                    B. 1
                   y = 3       Divide each side by 7.                 7
                                                                   C. 11                 D. 7

                                                                     Answer
                   Answer              x = 6; y = 3
                                                                   Find b.
                                                                   A. 0.5                B. 1.5

                                                                   C. –6                 D. 1
                Your Turn!                                           Answer


               Midsegment of a Triangle
                 Triangle UXY has vertices U(–3, 1), X(3, 3) and                       y      X
                 Y(5, –7). WZ is a midsegment of △UXY. Find the                    W             (3, 3)
                 coordinates of W and Z.
                                                                        (–3, 1)
                                                                            U
                 A. W (0, 1), Z (1, –3)
                 B. W (0, 2), Z (2, –3)
                 C. W (0, 3), Z (2, –3)                                            O                    x
                 D. W (0, 2), Z (1, –3)                                                Z


                   Answer
                                                                                                     (5, –7)
                                                                                                     Y

                 Triangle UXY has vertices U(–3, 1), X(3, 3) and    Triangle UXY has vertices U(–3, 1), X(3, 3) and
                 Y(5, –7). WZ is a midsegment of △UXY.            Y(5, –7). WZ is a midsegment of △UXY.
                                                                         1
                 Is WZ || XY?                                     Is WZ =      XY?
                                                                         2
                 A. Yes                                           A. Yes
                 B. No                                            B. No




                   Answer                                           Answer








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