Questions and Answers
What defines an irregular polygon?
Not having equal interior and exterior angle measures and/or side lengths
Which term best describes a polygon with at least one interior angle greater than 180 degrees?
Concave
How is an irregular polygon named based on the number of sides?
By the number of sides
Which of the following shapes is an example of an irregular polygon?
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What characteristic of irregular polygons distinguishes them from regular polygons?
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What is a defining characteristic of a trapezoid?
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Why is a non-square rectangle considered an irregular polygon?
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In which case would a figure qualify as an irregular polygon?
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What makes regular polygons different from irregular polygons?
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What is true about all regular polygons?
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Study Notes
Trapezoids and Polygons
- A trapezoid is a closed figure with four sides, but only one set of parallel sides, which are not equal.
- The four angle measures in trapezoids are also not equal.
- Trapezoids are irregular polygons.
Irregular Polygons
- Irregular polygons are polygons whose interior and exterior angle measures are not equal and/or whose side lengths are not equal.
- Three characteristics of irregular polygons:
- All sides and all angles are not equal
- Angles are equal but sides are not
- Sides are equal but angles are not
- Concave polygons are always irregular polygons.
- Irregular polygons can have equal sides, but not equal angles (e.g., rhombus).
- Irregular polygons can have equal angles, but not equal sides (e.g., non-square rectangle).
Regular Polygons
- Regular polygons have all side lengths equal and all interior and exterior angle measures equal.
- Both criteria about the sides and the angles must be met for the polygon to be regular.
- Regular polygons are always convex figures, meaning all interior angles are less than 180 degrees.
Examples of Polygons
- Quadrilateral ABCD is a regular polygon (square) because each angle is 90 degrees and all side lengths are 2 units.
- Pentagon HIJKL is a regular polygon because each angle measures 108 degrees and all side lengths are 2.5 units.
- Triangle EFG is a regular polygon (equilateral triangle) because each angle measures 60 degrees and all side lengths are 3 units.
Irregular Polygon Examples
- Trapezoids
- Non-square rectangles
- Non-equilateral triangles
- Concave polygons (e.g., irregular pentagon)
- Irregular polygons in the natural world (e.g., shape of a cell phone or laptop)
