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Is a Square a Rectangle?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Number the Sides

Age 7 to 11 Challenge Level:

The triangles in this set are 'similar':

first set of triangles


'Similar' means that the triangles are exactly the same shape, but not the same size. The sides are in the same ratio to each other. (Note that these triangles are not drawn to scale.)

What can you say about the length of the side of the third triangle which is marked with a question mark? Of course the triangles could be different ways up, too:

same as first set but different orientation


There are five more sets of similar triangles below. Can you work out the lengths of the sides marked with a question mark?

Set 2:



Set 3:



Set 4:



Set 5:



Set 6: