Rigid vs Flexible Shapes Math Example 3

Solution

1. 1
   Step 1: A rectangle is a quadrilateral with four sides. Even with fixed side lengths, a quadrilateral has $n - 3 = 4 - 3 = 1$ degree of freedom — it can deform into a parallelogram by shearing.
2. 2
   Step 2: Adding a diagonal brace divides the rectangle into two triangles. A triangle has $3 - 3 = 0$ degrees of freedom when its side lengths are fixed, making it rigid by SSS.
3. 3
   Step 3: Since both triangles are individually rigid and share the diagonal brace, the entire gate structure becomes rigid and can no longer sag or rack.