Geometrical Structures Vocabulary

Fundamental Components: Points, Lines, and Angles

  • Point: This is defined as a specific location within a given space.
  • Line: This is the resulting product of a single point moving continuously along a specific path.
  • Straight Line: This represents the shortest possible distance existing between any 22 points.
  • Horizontal Line: A line that is specifically drawn from a leftward to a rightward direction.
  • Vertical Line: A line specifically drawn from the top-most point to the bottom-most point.
  • Inclined Line: This refers to a line that is oriented diagonally.
  • Perpendicular Lines: These are lines that intersect or meet to form exact 9090^{\circ} angles with one another.
  • Parallel Lines: These are lines positioned side by side that will never intersect or meet, regardless of how far they are extended in either direction.
  • Curve Line: This refers to any line that is not straight in its trajectory.
  • Arc: This is a connected section taken from the total circumference of a circle.
  • Circle: A closed geometric figure that is bounded by exactly one curved line.
  • Angle: This geometric figure is formed whenever two lines intersect or meet.
  • Straight Angle: An angle that measures exactly 180180^{\circ}.
  • Right Angle: An angle that measures exactly 9090^{\circ}.
  • Acute Angle: An angle whose measure is strictly less than 9090^{\circ}.
  • Obtuse Angle: An angle whose measure is strictly greater than 9090^{\circ}.

Detailed Geometry of Circles

  • Circles: A circle is defined as the complete set of all points in a plane that are located at a specific, given distance from a fixed point known as the center.
  • Diameter: A straight line that passes directly through the center of the circle, connecting two points on the boundary.
  • Radius: This is a line segment extending from the center of the circle to any point located on the circle's boundary.
  • Chord: A line segment where both endpoints lie on the boundary of the circle.
  • Segment: A specific portion of a circle that is bounded by a combination of an arc and a chord.
  • Tangent: A straight line that intersects the boundary of a circle at exactly one (11) point.
  • Secant: A straight line that passes through two (22) points on the circle's boundary but does not pass through the center.
  • Quadrant: A specific part of a circle bounded by two radii forming a 9090^{\circ} angle; it constitutes exactly 14\frac{1}{4} of the total circle.
  • Sector: A part of a circle that is bounded by two radii and a connecting arc.
  • Concentric Circles: These are two or more circles that share a common center point.
  • Eccentric Circles: These are circles located inside another circle that possess different center points.

Classification and Properties of Polygons

  • Polygon: A closed geometric figure consisting of a sequence of straight lines.
  • Regular Polygon: A polygon in which all sides are of equal length.
  • Irregular Polygon: A polygon characterized by sides of unequal lengths.

Specific Types of Triangles

  • Triangle: A polygon defined by having three (33) sides and three (33) angles.
  • Equilateral Triangle: A triangle where all three sides are equal in length.
  • Isosceles Triangle: A triangle where exactly two (22) sides are equal in length.
  • Right Triangle: A triangle that contains one angle measuring exactly 9090^{\circ}.
  • Scalene Triangle: A triangle in which no sides are equal and no angles are equal.

Identification and Types of Quadrilaterals

  • Quadrilateral: A polygon defined by having four (44) sides and four (44) angles.
  • Parallelogram: A quadrilateral featuring two distinct pairs of parallel sides.
  • Square: A quadrilateral with four (44) equal sides and four angles that each measure 9090^{\circ}.
  • Rectangle: A quadrilateral with two unequal pairs of parallel lines and four angles that each measure 9090^{\circ}.
  • Rhombus: A quadrilateral with four (44) equal sides where the internal angles do not measure 9090^{\circ}.
  • Rhomboid: A type of parallelogram where the internal angles do not measure 9090^{\circ}.
  • Trapezoid: A quadrilateral featuring exactly one pair of unequal parallel lines and internal angles that do not measure 9090^{\circ}.
  • Trapezium: A quadrilateral with unequal sides and no parallel lines.

Nomenclature of Polygons by Side Count

  • Pentagon: A polygon with five (55) sides.
  • Hexagon: A polygon with six (66) sides.
  • Heptagon: A polygon with seven (77) sides.
  • Octagon: A polygon with eight (88) sides.
  • Nonagon: A polygon with nine (99) sides.
  • Decagon: A polygon with ten (1010) sides.