Solid Mensuration - Study Notes


Basic Geometric Terminology: Point, Line, Planes & Angles

  • The most basic terms in mensuration

  • 1) Point

    • A zero-dimensional object with position only; has no length, width, or thickness

    • Examples: Point A, Point B, Point C

  • 2) Line

    • A one-dimensional figure with no thickness, extending in both directions

  • 3) Ray

    • A straight line that is limited from one side and infinite from the other

    • Notation example:

    • Ray AB lies from A through B and beyond

  • 4) Segment (Line Segment)

    • Part of a straight line bounded on both ends

    • Notation example: AB

  • 5) Parallel lines

    • Straight lines lying in the same plane that do not intersect no matter how far extended

  • 6) Intersecting lines

    • Two or more lines that meet at a common point

  • 7) Transversal line

    • A line that cuts across two or more lines

  • 8) Broken lines

    • A set of line segments connected end to end

  • 9) Collinear points

    • Points lying on the same line

  • 10) Midpoint

    • The point exactly halfway between two endpoints of a line segment

  • 11) Plane

    • A flat surface with length and width but no thickness

  • 12) Intersections of planes

    • If two planes intersect, their intersection is a straight line

  • 13) Parallel planes with a third plane

    • The intersections are parallel lines

  • 14) Planes perpendicular to a third plane

    • If two planes are perpendicular to the third plane, their intersection is also perpendicular to that plane

  • 15) Coplanar points

    • Points that lie on the same plane

Angle Theory: Points, Lines, Planes & Angles (Detailed)

  • 17) An angle is a space formed by two rays (sides) sharing a common endpoint called the vertex

  • 18) Angle Measurements and Units:

    • Degree (°): One complete revolution is divided into 360 parts: 360360 parts; symbol: exto^ ext{o}

    • Radian (rad): One complete revolution equals 2 extπ2\, ext{π} radians

    • Gradient (grad): One complete revolution divided into 400 parts

    • Mil (mil): One complete revolution divided into 6400 parts

  • 19) Forms of Angles:

    • Acute angle: less than 90exto90^ ext{o}

    • Right angle: exactly 90exto90^ ext{o}

    • Obtuse angle: more than 90exto90^ ext{o} and less than 180exto180^ ext{o}

    • Straight angle: 180exto180^ ext{o}

    • Reflex angle: more than 180exto180^ ext{o} but less than 360exto360^ ext{o}

  • 20) Additional Forms of Angle (continued):

    • Complementary angles: two angles whose sum is 90exto90^ ext{o}

    • Supplementary angles: two angles whose sum is 180exto180^ ext{o}

  • 21) Interior and exterior angles with parallel lines and a transversal

  • 22) Alternate interior angles: a pair of non-adjacent interior angles on opposite sides of the transversal

  • 23) Dihedral angle: the amount of divergence of two intersecting planes