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Homework Help Math Geometry Vocabulary

To understand the complicated geometry terms, you need to understand the basics first. Here are 15 basic geometry terms to help you get a decent foundation for everything else.

  • A line
  • A straight line drawn at any angle.

  • A plane
  • This is a two-dimensional platform. It has length and breadth, but no depth.

  • A foot
  • When a line intersects with a plane, that is called a foot.

  • A parallelogram
  • A shape that has four sides. Each side has the same length as its opposite counterpart.

  • Diagonal
  • When a closed shape has a line on the inside of it that stretches from one corner to another, that line is called a diagonal. Note that this does not apply to two corners that are next to each other—because drawing a line form one corner to the one next to it is called an edge; therefore this can only be done on a shape that has four or more corners.

  • Bisect
  • A dividing line drawn across lines, corners, and/or shapes.

  • A square
  • Where all four sides are perfectly perpendicular to each other in length. All four corners are also exactly 90 degrees.

  • A triangle
  • A closed shape with three sides and three corners. All three corners of a triangle will always make up 180 degrees.

  • A coplanar
  • A 2 dimensional surface that is shaped like a triangle.

  • An incenter
  • If you bisected a triangle from each corner and met each line in the middle, you could then draw a perfect circle which would connect the three points of the lines that meet each side. This is called the incenter.

  • Perpendicular
  • Where two opposite sides are symmetrically lined up with each other.

  • A kite
  • Imagine the shape of a kite. It has two short sides that are the same length and perpendicular to each other. Then it has two more sides that are longer, but also the same length and perpendicular to each other.

  • Altitude of a triangle
  • When you pull a line from one corner of a triangle to its adjacent side, that line refers to the altitude of a triangle.

  • Orthocentre
  • If you did the above with all three corners, the middle point of the triangle would be called the orthocentre.

  • Collinear
  • Two points that appear on the same line are called collinear.

    GEOMETRY GLOSSARY

    Mr. X is glad to provide video presentations of hundreds of geometry glossary terms. The geometry glossary is part of a complete math glossary available free of charge on the website. All geometry glossary terms are provided free of charge to all users.

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    TitleDescription
    AAS Congruence Angle-angle-side congruence between two (or more) triangles.
    Congruent triangles have sides and angles of identical measure.
    AbscissaThe horizontal axis, or the first coordinate in an ordered pair.
    Acute AngleAn angle whose measure is less than 90 degrees.
    Acute Triangle A triangle whose interior angles are each acute, that is, less than 90 degrees (or π/2 radians).
    Adjacent Next to each other.
    The idea is especially important in geometry, as with adjacent angles that share a common ray.
    Adjacent Angles Next to each other.
    Adjacent angles share a common ray and subsequently have a common vertex.
    Alternate Exterior Angles Given two parallel lines cut by a transversal, angles exterior to the parallel lines and on opposite (alternate) sides of the transversal are congruent.
    Alternate Interior Angles Given two parallel lines cut by a transversal, angles interior to (between) the parallel lines and on opposite (alternate) sides of the transversal are congruent.
    Altitude Height.
    The perpendicular or orthogonal distance above a fixed reference, as height above mean sea level.
    In geometry, the shortest distance from the base of an object to its apex (or top).
    Altitude of a Cone The shortest line segment from the apex (tip) of a cone to the plane of its base.
    Altitude of a Cylinder The distance between the planes containing the bases of a cylinder.
    Altitude of a Parellelogram The distance between opposite sides of a parallelogram
    Altitude of a PrismThe length of the shortest line segment between the planes containing the bases of a prism.
    Altitude of a Trapezoid The distance between bases of a trapezoid.
    Altitude of a TriangleThe shortest line segment between the vertex of a triangle and line containing the opposide of the triangle.
    The three altitudes of a triangle are concurrent at the orthocenter.
    Amplitude Periodic functions have an amplitude that is half the range between the highest and lowest values.
    The height a sinewave climbs from zero (if zero is its mean values) is its amplitude.
    Analytic Geometry Effectively coordinate geometry.
    It is the use of coordinates (in two or more dimensions) to determine geometric relationships.
    AngleThe separation of two rays measured as the rotation of one of the rays.
    Usually measured in either degrees or radians, other systems of measuring rotation are also used to assign values to angles.
    Angle BisectorA ray (or line) that divides an angle into two congruent halves.
    The three angle bisectors of a triangle are concurrent at the incenter.
    Angle of DepressionThe angle below a horizontal reference.
    Typically it is the angle between a line-of-sight ray referenced to a horizontal line (or plane).
    Angle of Elevation The angle above a horizontal reference.
    Typically it is the angle between a line-of-sight ray referenced to a horizontal line (or plane).
    AnnulusThe area, or region, between two concentric circles of different radii.
    ApexThe top.
    Most generally a singular situation as a point.
    The vertex of a cone or pyramid is an apex.
    ApothemThe apothem applies to a regular polygon; it is either the distance from the center to a midpoint of a side, or the radius of an inscribed circle in the polygon.
    ArcA section of circumference.
    An arc is measured either by its own length or with a central angle.
    Arc LengthA curved length; it can be the distance around a portion of a circle, or around a different shape of curved figure.
    AreaThe measure of a plane region defined to be within some boundary.
    Area of a CircleThe extent of surface contained within the circle; π times the square of the radius.
    Area of a KiteHalf the product of the diagonals.
    Area of a ParallelogramAkin to the area of a rectangle, the area of a parallelogram can be expressed as the product of length times width.
    Area of a RectangleThe extent of surface contained within the rectangle; length times width.
    Area of a Regular PolygonOne-half the product of perimeter times the apothem.
    Remember that regular means equilateral and equiangular.
    Area of a RhombusIf s is the length of a side and h is the height, s-squared times the sine of the big interior angle; s-squared times the sine of the smaller interior angle; half the product of the diagonals.
    Area of a Sector of a CircleIt is the surface area of a slice of pie.
    We like arc length s=rΘ.
    So area of a sector is r-squared times theta all over two (Θ in radians).
    Area of a Segment of a CircleGiven central angle theta, area of the segment is one-half the square of the radius times the quantity (Θ minus sine Θ), provided Θ is in radians.
    Area of a TrapezoidOne-half the (sum of the bases) times the height.
    Or, the product of (median) and (altitude).
    Area of a TriangleOne-half times the base times the height.
    Also, given perimeter a+b+c, and semiperimeter s=half that sum, then area = the square root of [s times (s-a) times (s-b) times (s-c)].
    (Heron).
    Area of an EllipseIf 2a and 2b are the lengths of the major and minor axes of the ellipse, then the area of the ellipse is simply πab.
    Area of an Equilateral TriangleGiven side of length s, the area of an equilateral triangle is s-squared times the-square-root-of-three over four.
    ASA CongruenceAngle-side-angle congruence between two (or more) triangles.
    Congruent triangles have sides and angles of identical measure.
    AxiomAccepted without proof (unlike a theorem), an axiom is readily understood and regarded as fact.
    AxisIn physics, a line about which a body rotates.
    In mathematics, a line that divides a plane or space into two equal halves, typically demarcated in units.
    Axis of RotationA line about which a body rotates.
    Axis of SymmetryA line about which a graph or body is symmetrical, that is, a mirror image on one side of the axis from the body or graph on the other side.

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