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A The lengths of the three sides of a right-angled triangle such as (3, 4, 5) and
(8, 15, 17) are known as Pythagorean triples.
You can explore the Pythagorean triples through the following activity.

Open the folder downloaded from page vii for this activity.

1. Open the file Triples.ggb using GeoGebra.
2. Is the triangle shown a right-angled triangle?
3. Click and drag the slider m and the slider
n and observe the changes on the screen
displayed.
4. Do the lengths of sides shown constitute a
set of triples?

5. Click and drag the slider m and the slider n
for other combinations.
6. Explain what you have observed.

7. Present your findings in class.

B Constructing a Pythagorean Tree
A Pythagorean tree is a pattern constructed based on right-angled triangles and
squares related to Pythagoras’ theorem. The Pythagorean tree was invented by a Dutch
mathematics teacher in 1942.

CHAPTER
13
Construct your own Pythagorean tree beginning from a right-angled triangle with
squares drawn on each side of the triangle. Then similar triangles are drawn on the
sides of the squares. Then squares are drawn on the sides of the new triangles and
so on.

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Chapter 13

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