Figure 1 below shows a pair of horizontal parallel lines and a pairof parallel t

Question

Figure 1 below shows a pair of horizontal parallel lines and a pairof parallel transversals. One parallelogram (A1) is formed. A third parallel transversal is added to the diagram as shown inFigure 2. Three parallelograms are formed Drawing additional transversals will form new parallelograms. Two transversals will form 1 parallelogram, 3 will form 3parallelograms, 4 will form 6 parallelograms, 5 will form 10, 6will form 15, and 7 will form 21. Find a relation between thenumber of transversals and the number of parallelograms and find ageneral statement. Next consider the number of parallelograms formed by threehorizontal parallel lines intersected by parallel transversals.Develop and test another general statement for this case. Now extend your results to m horizontal parallel lines interectedby n parallel transversals. Find the general statement for theoverall pattern. I figured out most of this problem but I found that the generalstatement for the relationship between the number of transversalsand the number of parallelograms and the relationship between thenumber of horizontal parallel lines and the number ofparallelograms is the same. For both I go the general statement y =.5x^2- .5x I'm not sure if both are suppose to be the same. Also,I'm not sure what it means when it says to find the generalstatement for the overall pattern.

Explanation / Answer

It is the same (just turn your head so that the transversals lookhorizontal, and now the old horizontals are transversals). n(n-1)/2 For the general case we now have n horizontal lines, and mtransversals we'll get [n(n-1)/2]*[m(m-1)/2]

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