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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Triangle Transformation

Draw a triangle on a piece of paper, and cut it out.

**Can you find a way to cut your triangle into no more than four pieces, and reassemble the pieces to make a rectangle?**

Is it always possible, no matter what triangle you start with?

If you don't know where to start, click below to see some prompts that may help you:

First prompt:

Start with an isosceles triangle. How could you make it into a rectangle?

Is there a relationship between the base and height of your triangle, and the base and height of the rectangle?

Second prompt:

Draw any triangle, find the midpoints of two of the sides, and join them together. What do you notice?

Third prompt:

Once you have joined the midpoints, can you rearrange the pieces to make a parallelogram? Does that help you to create a rectangle?

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Age 7 to 14

Challenge Level

Draw a triangle on a piece of paper, and cut it out.

Is it always possible, no matter what triangle you start with?

If you don't know where to start, click below to see some prompts that may help you:

First prompt:

Start with an isosceles triangle. How could you make it into a rectangle?

Is there a relationship between the base and height of your triangle, and the base and height of the rectangle?

Second prompt:

Draw any triangle, find the midpoints of two of the sides, and join them together. What do you notice?

Third prompt:

Once you have joined the midpoints, can you rearrange the pieces to make a parallelogram? Does that help you to create a rectangle?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?