Identifying Polygons - ISEE Lower Level: Mathematics Achievement

Heptagon. Heptagons are defined by having seven sides, following the systematic naming based on Greek numerals for polygons.

Octagon. The term originates from 'octo' meaning eight, applied to polygons composed of eight straight line segments.

Nonagon. 'Nona' prefix signifies nine, used for polygons with exactly nine sides in geometric classification.

Decagon. Decagons are identified by their ten sides, with naming rooted in the Greek 'deka' for ten.

Dodecagon. Dodecagons feature twelve sides, named using 'dodeca' from Greek for twelve in polygon terminology.

A polygon with all sides and all angles congruent. Regularity in polygons requires uniformity in side lengths and interior angles, ensuring symmetry.

A polygon that is not regular. Irregularity arises when a polygon lacks uniformity in all sides or all angles, distinguishing it from regular forms.

A polygon with all interior angles less than $180^\circ$. Convexity ensures no interior angle exceeds $180^\circ$, preventing the polygon from caving in on itself.

A polygon with at least one interior angle greater than $180^\circ$. Concavity occurs when at least one interior angle measures more than $180^\circ$, creating a dent in the shape.

Parallelogram. Parallelograms are defined by having two pairs of parallel opposite sides, which also implies equal opposite angles.

Trapezoid. Trapezoids feature precisely one pair of parallel sides, known as bases, with the other sides nonparallel.

Isosceles trapezoid. Isosceles trapezoids have equal-length nonparallel sides, leading to base angles being congruent.

Rectangle. Rectangles are equiangular quadrilaterals with all angles at $90^\circ$, ensuring opposite sides are equal and parallel.

Rhombus. Rhombi are equilateral quadrilaterals where all sides are of equal length, with opposite angles equal.

Square. Squares combine properties of rectangles and rhombi, being both equilateral and equiangular with $90^\circ$ angles.

Kite. Kites have two pairs of equal adjacent sides, resulting in one pair of equal opposite angles and perpendicular diagonals.

Rectangle. This shape qualifies as a rectangle due to its parallel opposite sides and right angles, forming a special parallelogram.

Rhombus. The figure is a rhombus because its equal sides and parallel opposites align with the definition of an equilateral parallelogram.

Isosceles trapezoid. Congruent nonparallel sides in a trapezoid define it as isosceles, ensuring equal base angles and symmetric properties.

Kite. Two pairs of adjacent equal sides without overall equilateralism characterize a kite, distinguishing it from rhombi.

Regular pentagon. A pentagon becomes regular when all sides and angles are equal, exhibiting rotational symmetry of order five.

Hexagon. Hexagons derive their name from the Greek 'hex' for six, referring to polygons with precisely six sides.

Pentagon. The prefix 'penta' in polygon nomenclature indicates five equal or unequal straight sides forming a closed figure.

Quadrilateral. Polygons are named according to their side count, using 'quadri' for four straight sides enclosing an area.