- Cut 4 congruent right angled triangles from some scrap paper.
- Arrange them as shown in diagram 1 in your notebook.
- What do you notice about the quadrilateral labelled 5?
- Draw the square frame that this arrangement fits into exactly.
- How can you be sure that the frame is a square?
- Place the 4 triangles inside the square frame as in diagram 2.
- What do you notice about the quadrilateral labelled 6 and 7?
- What can you deduce about the areas of quadrilaterals 5, 6 & 7.
- Does the same hold for any 4 congruent right angled triangles?
- What have you proved?
These 4 congruent triangles are arranged in the squares shown in the diagrams all of which have sides (a + b).
Just take away the four identical right angled triangles from each of the diagrams. What is left?
How can you be sure that the shapes labelled 5, 6 and 7 are squares?
What does this tell you about the area of square 5 compared with the areas of squares 6 and 7?
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Can you also use the diagram showing shapes 1, 2, 3, 4, 6 and 7 to show that
(a + b)^2 = a^2 + b^2 + 2ab?