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Depth 1 · 83 s

Straight sides, closed

A polygon is a flat shape closed by straight sides - no gap, no curve, no crossing. It is named by its number of sides, and it is regular when all its sides and all its angles are equal.

About this video

What do a warning sign, a stop sign and the cells of a honeycomb have in common? They are all polygons. This animation builds one side by side: straight line segments, joined end to end until the shape comes back to where it started. Then it shows three shapes that are not polygons, each for a different reason: one has a gap, so it is not closed; a circle has a curved edge; and a shape whose sides cross in the middle breaks the rule that sides meet only at their ends.

Next it counts. A pentagon's five sides light up one by one, then its five vertices, the corners where two sides meet. A polygon always has as many vertices as sides, because each side ends at a vertex and each vertex joins two sides. Polygons are named by that number: triangle, quadrilateral, pentagon, hexagon and octagon.

Last, regular polygons. A regular polygon has all its sides equal and all its angles equal, and both must be true. A long rectangle has four equal angles but not four equal sides. A rhombus leaning over has four equal sides but not equal angles. A square has both, so it is a regular quadrilateral. Regular hexagons fit together with no gaps, which is why a honeycomb is made of them. This video goes with the Shapes with Straight Sides lesson of Geometry Level 1 on Knaph.

This video shows depth 1 of Polygons.

Learn Polygons

Transcript

  1. 0:00Signs, windows, honeycombs. What do these shapes share?
  2. 0:06Straight sides, joined end to end, until the shape closes. That is a polygon.
  3. 0:14A gap? Not a polygon.
  4. 0:19A curved edge? Not a polygon either.
  5. 0:24Sides that cross in the middle? Not a polygon.
  6. 0:30Count the sides. Five. Count the corners, the vertices. Five. Always the same number.
  7. 0:40Polygons are named by their sides. Triangle, quadrilateral, pentagon, hexagon, octagon.
  8. 0:58Regular means all sides equal and all angles equal. The rectangle has equal angles only. The rhombus has equal sides only. The square has both.
  9. 1:10Regular hexagons fit together with no gaps, like a honeycomb.
  10. 1:16Straight sides, closed. A polygon.