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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Diagonally Square

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Age 7 to 11

Challenge Level

Take a look at this image:

**What do you see?
What do you notice?**

Ayah has a conjecture. She thinks that the diagonals of the square meet at right angles.

**Do you agree? How could you find out?**

Draw another square and its diagonals.

Do the diagonals of your new square meet at right angles?

What happens if you draw another square and its diagonals?

**Do the diagonals of a square always meet at right angles?**

Mathematicians aren't usually satisfied with a few examples to convince themselves that something is always true.

**Can you create an argument that would convince mathematicians?**

Once you have had a good think about it, you might like to look at this proof that has been scrambled up.

Can you rearrange the steps into the correct order?

If you would prefer to work away from a screen, you could print off, cut up and rearrange the statements on this sheet (it includes two copies of each statement).

Toby has another conjecture. He says, "I know that a square is a special type of rectangle. So I think that the diagonals of rectangles meet at right angles too."

What do you think?

**Do the diagonals of a rectangle always meet at right angles?**

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do this?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.