How many triangles can be constructed with sides measuring 6 cm, 2 cm, and 7 cm?

One

Step-by-step explanation:

First you need to make sure that these sides will work with the triangle inequality.  Basically add two sides together and make sure that sum is greater than the other side.  Do this for all three sides.  

6+2>7

6+7>2

2+7>6

Since this does form at least one triangle you just have to imagine how you might reposition the sides to make a different triangle.  The catch is, if you do adjust one side  it makes a different triangle.  If you make a side longer then they don't match the measurements listed any more, and if you adjust the angle of any of the sides, the lines won't line up unless you adjust their size.  

One

Step-by-step explanation: