Construction - September 2005, Stage 3&4

Problems

problem icon

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?

problem icon

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?

problem icon

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...

problem icon

Three Tears

Stage: 4 Challenge Level: Challenge Level:1

Construct this design using only compasses

problem icon

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?

problem icon

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.