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Broad Topics >

Angles, Polygons, and Geometrical Proof > Similarity and congruence

##### Age 11 to 14 Challenge Level:

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

##### Age 11 to 14 Challenge Level:

A tennis ball is served from directly above the baseline (assume
the ball travels in a straight line). What is the minimum height
that the ball can be hit at to ensure it lands in the service area?

##### Age 11 to 14 Challenge Level:

If the sides of the triangle in the diagram are 3, 4 and 5, what is
the area of the shaded square?

##### Age 11 to 14 Challenge Level:

Draw all the possible distinct triangles on a 4 x 4 dotty grid.
Convince me that you have all possible triangles.

##### Age 11 to 14 Challenge Level:

Explain how the thirteen pieces making up the regular hexagon shown
in the diagram can be re-assembled to form three smaller regular
hexagons congruent to each other.

##### Age 7 to 11 Challenge Level:

The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?

##### Age 7 to 11 Challenge Level:

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

##### Age 11 to 16 Challenge Level:

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

##### Age 11 to 14 Challenge Level:

Make your own pinhole camera for safe observation of the sun, and find out how it works.