Constructing Triangles
Eugena from City of London School for Girls made a good start to this problem:
Say you roll three dice and you end up with the numbers 6, 3 and 1.
You draw the 6cm line and then with a compass and ruler you measure 3cm.
After you draw the arc, you repeat the same step, the only change being that
instead of measuring 3cm you measure 1cm.
Draw the arc and you'll see that the two arcs will not intercept.
The three numbers didn't work...
Say you roll three dice and you end up with the numbers 5, 3 and 6.
You draw the 5cm line and then with a compass and ruler you measure 3cm.
After you draw the arc, you reapeat the same step, the only change being that
instead of measuring 3cm you measure 6cm.
Draw the arc and you'll see that this time the arcs intercept.
The three numbers worked!
But the key questions still remain:
When is it possible to construct a triangle from the three numbers generated?
Is there a quick way to tell if it will be possible to construct a triangle?
Do send us your thoughts.