This applet allows you to see why certain triangles are 'possible' and why certain triangles are 'impossible'. Use the black slider to adjust the length of the base side, and the other two sliders to adjust the other two sides. When the 'Magic' checkbox is checked, you can see the circles drawn in. You will notice that when they intersect, the point of intersection is precisely the point that joins the two other sides of a triangle. However, if the two circles do not intersect, then the triangle is impossible to construct.
Question 1: Is a triangle with sides 3, 4, 5 possible or impossible? Question 2: Is a triangle with sides 3, 2, 8 possible or impossible? Question 3: Is a triangle with sides 2, 3, 5 possible or impossible? Challenge 1: Play around with the applet, then come up with a rule to decide if a triangle is possible or impossible. Use your rule to test if the triangle 3, 4, 8 will be possible or impossible Challenge 2: Make a triangle where one side is 1 and the other side is 3. Make another triangle where one side is 1 and the other side is 4. Make a third triangle where one side is 1 and the other side is 5. What do you notice about the third side of each of these triangles? What do you think the third side will be for a triangle with sides 1 and 6?