# Parallelograms. This investigation will focus on the number of parallelograms formed by intersecting lines also knows as transversals.

Parallels and Parallelogram

Internal Assessment

By: Olivia Bloch

This investigation will focus on the number of parallelograms formed by intersecting lines also knows as transversals. Figure 1 below shows a pair of horizontal parallel lines and a pair of parallel transversals.  One parallelogram (A1) is formed. This figure with two transversals and two horizontal lines will be transformed by adding more transversals, and hence establishing the relationship between the number of transversals and parallelograms. The parallelogram is indicated in red.

Figure 2 below demonstrates how adding one transversal can form 3 parallelograms, and these are indicated in red, blue, and green.

Six parallelograms are then formed when adding a fourth parallel transversal, as seen in figure 3. The different parallelograms have been done using different colors, and the set notation illustrates the color it belongs to.

The information above can be gathered in a table, as shown below.

From this data we can generate a graph using excel, in order to determine the type of sequence we are dealing with.

The graph above shows an exponential growth; hence, it is a quadratic sequence. Moreover, the figure to the right shows the features of a quadratic equations; therefore, in order to determine the general statement of the sequence, we can use a calculator as shown below.

Hence the formula for this sequence is ...