Practice Rigid vs Flexible Shapes in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Rigid shapes maintain their form under stress without deforming; flexible shapes can change shape when force is applied.
A triangle made of sticks is rigid. A rectangle made of sticks can collapse into a parallelogram.
Example 1
mediumExplain why a triangle is rigid but a quadrilateral is flexible. Then describe how triangulation is used in structural engineering to make bridges rigid.
Example 2
hardA triangular frame has sides 5, 7, 8 cm. A quadrilateral frame has sides 5, 6, 5, 6 cm. How many shapes can each frame make? Connect to degrees of freedom.
Example 3
mediumA carpenter builds a rectangular gate that sags over time. Explain why adding a diagonal brace fixes this, using the concept of rigid vs flexible shapes.
Example 4
easyA playground climbing frame is made of steel tubes in square panels. Why might this be unsafe, and how could it be improved?
Example 5
hardA hexagonal frame with all sides equal and all angles at 120° is rigid only if all angles are fixed. If the frame's joints are flexible (angles can change), how many degrees of freedom does it have, and how could you brace it minimally?