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Parallels and Parallelograms

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  • Essay length: 1904 words
  • Submitted: 29/08/2009
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International Baccalaureate Maths

The first 200 words of this essay...

QASMT

Mathematics IA

Parallels and Parallelograms

Jeremiah Joseph

24/05/2009

This internal assessment will investigate the relationship between vertical transversals, horizontal lines and parallelograms. Vertical transversals are lines that intersect horizontal lines. To create parallelograms two or more parallel vertical transversals needs to intersect with two or more horizontal lines. This is shown in figure 1.1 and figure 1.2.

Figure 1.1

Figure 1.2

These above figures demonstrate how vertical transversals (red) intersect with horizontal lines (black) to create parallelograms. These parallelograms are demonstrated in figure 1.1, A1, A2, A1 U A2. Furthermore, the parallelograms are illustrated in figure 1.2, A1, A2, A3, A1 U A2, A2 U A3, and A1 U A2 U A3. If parallel transversals are continually added an increasing number of parallelograms would be formed and a general formula can be deduced.

Vertical Transversals

Parallelograms

Notation

2

1

A1

3

3

A1, A2, A1 U A2

4

6

A1, A2, A3, A1 U A2, A2 U A3, A1 U A2 U A3

5

10

A1, A2, A3, A4, A1 U A2, A2

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