7.2.1 Applying Properties of Similar Triangles (continued)
Two lines are determined to be parallel using the Converse of the Triangle Proportionality Theorem in this example. The lengths of line segments on the
divided sides of the triangle are given. To determine if DB divides EC and AC
proportionally, find the ratios of the lengths of the line segments around points B and D . The ratio of AB to BC is 4. The ratio of ED to DC is 4. Since the ratios are proportional, AE || BD by the Converse of the Triangle Proportionality Theorem.
Example 3 Art Application
If three or more parallel lines intersect two transversals, then they divide the transversals proportionally. Look carefully at the proportion of the line segment lengths formed by the intersection of the transversals. The length of a line segment is determined using the Two-Transversal Proportionality Corollary in this example. It is given that PT || QU || RV || SW . The lengths of four line segments formed by the intersection of the transversals is given. To find the unknown length, set up a proportion involving the line segment of unknown length and the line segments with given lengths. Substitute the known segment lengths, cross multiply, and solve for QS . The solution yields QS = 13.456 cm.
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