College Geometry

Question

In the diagram below, ST⎯⎯⎯⎯⎯⎯⎯∥PQ⎯⎯⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯⎯⎯∥CD⎯⎯⎯⎯⎯⎯⎯⎯.  Furthermore, SP=5x−1,  QM=x−1,  TQ=x+5,  , and PL=2x+5.  Find the ratio of LC to MD.

(Note that the diagram may not be drawn to scale.)

a) 137

b) 713

c) 31

d) More information is needed to solve this problem.

e) 13

f) None of the above

Answer 1

The crucial piece of information needed to solve this problem is that parallel lines cut by transversals cut of line segments which are in proportion.

Set up the proportions and then substitute the given vales.

You will find 2 equal fractions involving x which can be solved for x.

Then the required ratio can be determined.