# Construction - September 2005, Stage 3&4

## Problems

##### Stage: 3 Challenge Level:

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

### Property Chart

##### Stage: 3 Challenge Level:

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?

### Shapely Pairs

##### Stage: 3 Challenge Level:

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...

### Three Tears

##### Stage: 4 Challenge Level:

Construct this design using only compasses

### Triangle in a Triangle

##### Stage: 4 Challenge Level:

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

### Half a Triangle

##### Stage: 4 Challenge Level:

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