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 2 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 90∘ 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 180∘.
- Right Angle: An angle that measures exactly 90∘.
- Acute Angle: An angle whose measure is strictly less than 90∘.
- Obtuse Angle: An angle whose measure is strictly greater than 90∘.
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 (1) point.
- Secant: A straight line that passes through two (2) 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 90∘ angle; it constitutes exactly 41 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 (3) sides and three (3) angles.
- Equilateral Triangle: A triangle where all three sides are equal in length.
- Isosceles Triangle: A triangle where exactly two (2) sides are equal in length.
- Right Triangle: A triangle that contains one angle measuring exactly 90∘.
- 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 (4) sides and four (4) angles.
- Parallelogram: A quadrilateral featuring two distinct pairs of parallel sides.
- Square: A quadrilateral with four (4) equal sides and four angles that each measure 90∘.
- Rectangle: A quadrilateral with two unequal pairs of parallel lines and four angles that each measure 90∘.
- Rhombus: A quadrilateral with four (4) equal sides where the internal angles do not measure 90∘.
- Rhomboid: A type of parallelogram where the internal angles do not measure 90∘.
- Trapezoid: A quadrilateral featuring exactly one pair of unequal parallel lines and internal angles that do not measure 90∘.
- Trapezium: A quadrilateral with unequal sides and no parallel lines.
Nomenclature of Polygons by Side Count
- Pentagon: A polygon with five (5) sides.
- Hexagon: A polygon with six (6) sides.
- Heptagon: A polygon with seven (7) sides.
- Octagon: A polygon with eight (8) sides.
- Nonagon: A polygon with nine (9) sides.
- Decagon: A polygon with ten (10) sides.