GeoGebra Pythagoras Exploration

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📐 Part 1: 2D Pythagoras Exploration

1. In GeoGebra, construct a right-angled triangle with sides 3cm and 4cm. What is the length of the hypotenuse?

2. Use Pythagoras' theorem to verify your answer from Question 1. Show your working:

3. A ladder is placed 2 metres from the base of a wall and reaches 5 metres up the wall. How long is the ladder?

5.39 metres

3.00 metres

7.00 metres

29.00 metres

4. In GeoGebra's algebra view, what formula would you enter to calculate the hypotenuse of a triangle with sides a = 6 and b = 8?

Formula: _________________________

📦 Part 2: 3D Pythagoras Applications

5. A rectangular box has dimensions 4cm × 3cm × 5cm. What is the length of the space diagonal (corner to opposite corner through the centre)?

6. For 3D Pythagoras problems involving a cuboid with sides a, b, and c, the space diagonal formula is:

d² = a² + b²

d² = a² + b² + c²

d = a + b + c

d² = a² + c²

7. A bird flies from one corner of a rectangular field (50m × 30m) to the opposite corner, then up 20m vertically. What is the total distance of the bird's diagonal flight path?

🤔 Part 3: Reflection and Real-World Connections

8. Describe one advantage of using GeoGebra to explore Pythagoras' theorem compared to using pen and paper:

9. Give an example from everyday life in New Zealand where you might need to use 3D Pythagoras calculations:

10. Challenge: A telecommunications tower is 45 metres tall. A support cable runs from the top of the tower to a point 20 metres from the base. If you need to replace this cable, how many metres of cable do you need to order? (Include 2 metres extra for connections)