Basic Geometric Elements and Concepts
Geometry is the science that studies the relationships and properties of geometric elements (the main ones being: point, line, and plane) in the plane and space.
Branches of Geometry
- Plane Geometry: The part of geometry that studies the relationships and properties of geometric planes.
- Descriptive Geometry: The part of geometry that studies the systems of representation.
Representation Systems
A set of elements that are used to represent space figures in the plane and then return them to their original position.
Fundamental Geometric Elements
- Point: The intersection of two lines.
- Line: The intersection of two planes.
- Plane: A geometric element defined by:
- Three points.
- Two intersecting or parallel lines.
- A line and a point, or three points.
Polygons
A polygon is a closed plane figure formed by a number of sides and angles.
- Regular polygon: Sides and angles are equal.
- Irregular polygon: Sides and angles are unequal.
Locus
A locus is a set of all elements that satisfy the same condition.
Circumference and Lines
- Circumference: The locus of points equidistant from the center plane; a flat, closed curve formed by infinite points which are equidistant from the center.
- Straight line: An infinite sequence of points in the same direction.
- Curved line: An infinite sequence of points in different directions.
- Segment: A straight portion between two points.
- Perpendicular Bisector: The locus of points on the plane that are equidistant from the ends of a segment; a line that divides a segment into two equal parts.
Angles
- Angle: The flat portion between two intersecting straight lines; the aperture formed by two lines when they intersect.
- Bisector: The locus of points in the plane equidistant from two intersecting lines; a line that divides an angle into two equal parts.
- Central Angle: An angle formed by two radii of a circle.
- Interior Angle: An angle formed by two chords of a circle.
- Exterior Angle: An angle formed by two tangents of a circle.
Circle Elements
- Diameter: A segment that divides a circle into two equal parts.
- Radius: A segment from the center to any point on the circumference.
- Chord: A segment joining two points on the circle.
- Tangent: A line or a circle is tangent to another when they touch at one point.
- Secant: A line or a circle is secant to another when they intersect at two points.
- Arc: A portion of a circle’s circumference.
Other Geometric Concepts
- Link: The effect of joining one or two lines with another circle.
- Sphere: The locus of points in space that are equidistant from the center.
- Acute Angle: An angle that measures less than 90º.
- Right Angle: An angle that measures 90º.
- Obtuse Angle: An angle that measures more than 90º.
Triangles
- Obtuse Triangle: A triangle that has an obtuse angle.
- Equilateral Triangle: A triangle that has three equal sides and, therefore, three equal angles (60º).
- Isosceles Triangle: A triangle that has two equal sides and one different side.
Quadrilaterals
- Quadrilateral: A polygon with four sides.
- Parallelogram: A quadrilateral with parallel sides in pairs.
- Square: A parallelogram with equal sides; a regular polygon with four sides.
- Rectangle: A parallelogram with parallel sides equal two by two and four equal angles.
- Rhombus: A parallelogram with equal sides and angles equal two by two.
- Rhomboid: A parallelogram with sides parallel and equal in pairs.
- Trapezoid: A quadrilateral with two parallel sides and two non-parallel sides.
- Isosceles Trapezoid: A trapezoid with two equal sides.
- Scalene Trapezoid: A trapezoid with four different sides.
- Right Trapezoid: A trapezoid with two right angles.
- Trapezium: A quadrilateral with all different sides and no parallel sides.
Proportions and Ratios
- Proportion: To draw a similar figure with similar dimensions; to make a ratio of two figures.
- Ratio: The geometric relationship in size between two figures.
- Apothem: A segment connecting the center of a circle with the midpoint of a side of a polygon.
Curves
- Oval: A flat, closed curve formed by four arcs equal two by two and, therefore, doubly symmetric.
- Ovoid: A flat, closed curve consisting of four arcs, two identical and two different, and therefore, only once symmetrical.
- Spiral: A plane curve caused by the circular motion of a point rotating uniformly around a particular nucleus, steadily increasing the turning radius.