40 part each shape by whether it has any porallel or perpendicular sides.

Certainly! Here's a comprehensive list of 40 geometric shapes categorized based on whether they have **parallel sides**, **perpendicular sides**, **both**, or **neither**. This classification primarily focuses on **polygons**, especially quadrilaterals, but also includes other regular and irregular shapes for a broader perspective. --- ### **1. Shapes with Both Parallel and Perpendicular Sides** 1. **Square** - **Parallel Sides:** Yes (both pairs) - **Perpendicular Sides:** Yes (all angles are 90°) 2. **Rectangle** - **Parallel Sides:** Yes (both pairs) - **Perpendicular Sides:** Yes (all angles are 90°) 3. **Rhombus** - **Parallel Sides:** Yes (both pairs) - **Perpendicular Sides:** Not necessarily (only if angles are 90°, making it a square) 4. **Regular Hexagon** (with certain orientations) - **Parallel Sides:** Yes (multiple pairs) - **Perpendicular Sides:** Yes (at specific angles) 5. **Regular Octagon** (with certain orientations) - **Parallel Sides:** Yes (multiple pairs) - **Perpendicular Sides:** Yes (at specific angles) 6. **Right Trapezoid** (also known as Right Trapezium) - **Parallel Sides:** Yes (one pair) - **Perpendicular Sides:** Yes (two right angles) 7. **Oblong** - **Parallel Sides:** Yes (both pairs) - **Perpendicular Sides:** Yes (all angles are 90°) 8. **Floor Tile (Square)** - **Parallel Sides:** Yes - **Perpendicular Sides:** Yes 9. **Brick Shape** - **Parallel Sides:** Yes - **Perpendicular Sides:** Yes 10. **Cube (as a projection)** - **Parallel Sides:** Yes - **Perpendicular Sides:** Yes --- ### **2. Shapes with Parallel Sides Only** 11. **Parallelogram** - **Parallel Sides:** Yes (both pairs) - **Perpendicular Sides:** No (angles are not 90°) 12. **Trapezoid (Trapezium)** - **Parallel Sides:** Yes (one pair) - **Perpendicular Sides:** No 13. **Isosceles Trapezoid** - **Parallel Sides:** Yes (one pair) - **Perpendicular Sides:** No 14. **Regular Hexagon** (alternative orientations) - **Parallel Sides:** Yes - **Perpendicular Sides:** No 15. **Regular Octagon** (alternative orientations) - **Parallel Sides:** Yes - **Perpendicular Sides:** No 16. **Regular Decagon** - **Parallel Sides:** Yes (multiple pairs) - **Perpendicular Sides:** No 17. **Trapezium (UK)** - **Parallel Sides:** Yes (one pair) - **Perpendicular Sides:** No 18. **Diamond Shape (Non-Square Rhombus)** - **Parallel Sides:** Yes (both pairs) - **Perpendicular Sides:** No 19. **Regular Dodecagon** - **Parallel Sides:** Yes - **Perpendicular Sides:** No 20. **Regular Heptagon** - **Parallel Sides:** No (seven sides) - **Perpendicular Sides:** No --- ### **3. Shapes with Perpendicular Sides Only** 21. **Right Kite** - **Parallel Sides:** No - **Perpendicular Sides:** Yes (at specific angles) 22. **Right Arrowhead** - **Parallel Sides:** No - **Perpendicular Sides:** Yes 23. **Right Irregular Quadrilateral** - **Parallel Sides:** No - **Perpendicular Sides:** Yes (some angles are 90°) 24. **L-Shape (Right Angle)** - **Parallel Sides:** No - **Perpendicular Sides:** Yes 25. **T-Shape (Right Angle)** - **Parallel Sides:** No - **Perpendicular Sides:** Yes 26. **Plus Sign (+)** - **Parallel Sides:** No - **Perpendicular Sides:** Yes 27. **Cross Shape** - **Parallel Sides:** No - **Perpendicular Sides:** Yes 28. **Letters (e.g., "L", "T", "E")** - **Parallel Sides:** No - **Perpendicular Sides:** Yes 29. **Doorframe Shape** - **Parallel Sides:** No - **Perpendicular Sides:** Yes 30. **Window Frame (with muntins)** - **Parallel Sides:** No - **Perpendicular Sides:** Yes --- ### **4. Shapes with Neither Parallel Nor Perpendicular Sides** 31. **Scalene Quadrilateral** - **Parallel Sides:** No - **Perpendicular Sides:** No 32. **General Irregular Polygon (e.g., irregular pentagon)** - **Parallel Sides:** No - **Perpendicular Sides:** No 33. **Concave Quadrilateral** - **Parallel Sides:** Varies - **Perpendicular Sides:** Varies 34. **Star Polygon (Non-Regular)** - **Parallel Sides:** No - **Perpendicular Sides:** No 35. **Irregular Hexagon** - **Parallel Sides:** No - **Perpendicular Sides:** No 36. **Irregular Octagon** - **Parallel Sides:** No - **Perpendicular Sides:** No 37. **Asymmetrical Arrow Shape** - **Parallel Sides:** No - **Perpendicular Sides:** No 38. **Freeform Shape (Abstract Art)** - **Parallel Sides:** No - **Perpendicular Sides:** No 39. **Organic Shapes (e.g., Leaves, Amoeba)** - **Parallel Sides:** No - **Perpendicular Sides:** No 40. **Irregular Star Shapes** - **Parallel Sides:** No - **Perpendicular Sides:** No --- ### **Key Definitions** - **Parallel Sides:** Two sides are parallel if they are the same distance apart over their entire length and will never meet, no matter how far they are extended. - **Perpendicular Sides:** Two sides are perpendicular if they intersect at a 90-degree angle. ### **Notes** - **Regular Polygons:** These are shapes where all sides and angles are equal (e.g., regular hexagon, regular octagon). Depending on the number of sides and the orientation, some regular polygons have multiple pairs of parallel sides. - **Irregular Polygons:** These have sides and angles that are not all equal. Their classification regarding parallel or perpendicular sides varies based on their specific geometry. - **Non-Polygon Shapes:** Shapes like circles and ellipses do not have sides and therefore do not fall into these categories. This categorization can help in understanding the properties of various shapes, especially in fields like geometry, design, architecture, and art.