The triangle inequality
Three lengths make a triangle only if each side is shorter than the other two put together. Move the sliders and watch the triangle form, flatten, and fall apart.
Drag the dots on B and C to reshape the triangle. Point A stays put.
Sides a = 4 and b = 5 stay fixed while c stretches from 1 to 9. As c approaches a + b, the peak sinks and the triangle collapses into a line.
c
a + b9
a + b − c
Height of C
Choose two side lengths. The third side has to be longer than their difference and shorter than their sum. Try a value for c to test it.
Lower bound |a − b|
Upper bound a + b