GEOMETRY GLOSSARY
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Title  Description  

AAS Congruence  Angleangleside congruence between two (or more) triangles. Congruent triangles have sides and angles of identical measure. 

Abscissa  The horizontal axis, or the first coordinate in an ordered pair. 

Acute Angle  An 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 Prism  The 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 Triangle  The 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. 

Angle  The 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 Bisector  A 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 Depression  The angle below a horizontal reference. Typically it is the angle between a lineofsight ray referenced to a horizontal line (or plane). 

Angle of Elevation  The angle above a horizontal reference. Typically it is the angle between a lineofsight ray referenced to a horizontal line (or plane). 

Annulus  The area, or region, between two concentric circles of different radii.  
Apex  The top. Most generally a singular situation as a point. The vertex of a cone or pyramid is an apex. 

Apothem  The 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.  
Arc  A section of circumference. An arc is measured either by its own length or with a central angle. 

Arc Length  A curved length; it can be the distance around a portion of a circle, or around a different shape of curved figure.  
Area  The measure of a plane region defined to be within some boundary.  
Area of a Circle  The extent of surface contained within the circle; π times the square of the radius. 

Area of a Kite  Half the product of the diagonals.  
Area of a Parallelogram  Akin to the area of a rectangle, the area of a parallelogram can be expressed as the product of length times width.  
Area of a Rectangle  The extent of surface contained within the rectangle; length times width. 

Area of a Regular Polygon  Onehalf the product of perimeter times the apothem. Remember that regular means equilateral and equiangular. 

Area of a Rhombus  If s is the length of a side and h is the height, ssquared times the sine of the big interior angle; ssquared times the sine of the smaller interior angle; half the product of the diagonals. 

Area of a Sector of a Circle  It is the surface area of a slice of pie. We like arc length s=rΘ. So area of a sector is rsquared times theta all over two (Θ in radians). 

Area of a Segment of a Circle  Given central angle theta, area of the segment is onehalf the square of the radius times the quantity (Θ minus sine Θ), provided Θ is in radians. 

Area of a Trapezoid  Onehalf the (sum of the bases) times the height. Or, the product of (median) and (altitude). 

Area of a Triangle  Onehalf 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 (sa) times (sb) times (sc)]. (Heron). 

Area of an Ellipse  If 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 Triangle  Given side of length s, the area of an equilateral triangle is ssquared times thesquarerootofthree over four. 

ASA Congruence  Anglesideangle congruence between two (or more) triangles. Congruent triangles have sides and angles of identical measure. 

Axiom  Accepted without proof (unlike a theorem), an axiom is readily understood and regarded as fact.  
Axis  In 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 Rotation  A line about which a body rotates.  
Axis of Symmetry  A 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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