Construction - September 2005, Stage 3&4

Problems

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Keep Your Distance

Stage: 3 Challenge Level: Challenge Level:1

Can you mark 4 points on a flat surface so that there are only two different distances between them?

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Property Chart

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

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Shapely Pairs

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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Three Tears

Stage: 4 Challenge Level: Challenge Level:1

Construct this design using only compasses

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Triangle in a Triangle

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you work out the fraction of the original triangle that is covered by the inner triangle?

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Half a Triangle

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

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