Varignon Parallelogram Half Area Proof
This animation shows an arbitrary quadrilateral with the midpoints of its four sides connected in order, forming an inner parallelogram known as the Varignon parallelogram. Using diagonal triangles and midsegment properties, it visually demonstrates why this inner shape always has exactly half the area of the original quadrilateral, regardless of its shape. Useful for 9th graders studying geometry, midsegments, and area relationships through a clear, step-by-step visual proof.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
If the mid-points of the sides of a 4-gon (also known as a quadrilateral, but we prefer to call it a '4-gon') are joined in order, prove that the area of the parallelogram thus formed will be half of the area of the given 4-gon. Audience: 9th grader
Make the next one in this series
- Show why the Varignon parallelogram is always a parallelogram using the midsegment theorem.
- Demonstrate how the area ratio changes if midpoints are replaced with other fixed ratio points.
- Explore the Varignon parallelogram for a concave quadrilateral and check if the half-area rule still holds.
