NAME _____________________________________________ DATE ____________________________ PERIOD _____________ 7-5 Study Guide and Intervention Parallel Lines and Proportional Parts Proportional Parts within Triangles In any triangle, a line parallel to one side of a triangle separates the other two sides proportionally. This is the Triangle Proportionality Theorem. The converse is also true. = . If = , then XY RS If XY RS , then RX XT SY YT RX XT SY YT . If X and Y are the midpoints of RT and ST, then XY is a midsegment of the triangle. The Triangle Midsegment Theorem states that a midsegment is parallel to the third side and is half its length. RS. If XY is a midsegment, then XY RS and XY = 12 Example 1: In ABC, EF CB . Find x. = Since EF CB, FB AF AEEC x + 22 x+2 = 18 6 6x + 132 = 18x + 36 96 = 12x 8=x Chapter 7 29 Glencoe Geometry Example 2: In GHJ, HK = 5, KG = 10, and JL is one-half the length of LG. Is HJ KL ? Using the converse of the Triangle Proportionality Theorem, show that JL. HKKG = LG Let JL = x and LG = 2x. HKKG = 10 5= 1 2 LG JL= 2x x= 1 1 =1 , 2 Since 2 2 the sides are proportional and HJ KL . Exercises ALGEBRA Find the value of x. 1. 2. 3. 4. 5. 6. NAME _____________________________________________ DATE ____________________________ PERIOD _____________ 7-5 Study Guide and Intervention (continued) Parallel Lines and Proportional Parts Proportional Parts with Parallel Lines When three or more parallel lines cut two transversals, they separate the transversals into proportional parts. If the ratio of the parts is 1, then the parallel lines separate the transversals into congruent parts. If l1 l2 l3, If l4 l5 l6 and then ab c. u = v 1, then w = 1 Example: Refer to lines l1, l2, and l3 above. If a = 3, b = 8, and c = 5, find d. l1 l2 l3 so 38 = Exercis es ALGEBRA Find x and y. 1. 2. 3. 4. 5. 6. 5. d Then 3d = 40 and d = 131 . 3 x = d Chapter 7 30 Glencoe Geometry