Geometry Glossary

AA Theorem of Similarity

Two triangles are similar if two pairs of corresponding angles are congruent. hint: AA (_) of (_) (four words)

AAS Theorem of Congruence

Two triangles are congruent if two pairs of corresponding angles are congruent and a nonincluded pair of corresponding sides are congruent. hint: AAS (_) of (_) (four words)

Abscissa

The x-coordinate of a point in the coordinate plane; a member of the domain set.

Absolute value

For a number x, denoted |x| its distance from 0 on the number line. Thus, |x| always represents a nonnegative number. (two words)

Acute angle

An [angle] whose degree measure is greater than 0 and less than 90. (two words)

Acute triangle

A [triangle] with three acute angles. (two words)

Adjacent angles

Two [angles] that have the same vertex and share one side, but do not have any interior points in common. (two words, plural)

Alternate interior angles

Pairs of [angles] formed when a transversal intersects two lines. The two angles in each pair are between the two lines, have different vertices, and lie on opposite sides of the transversal. (three words, plural)

Altitude

A segment that is perpendicular to the side of the figure to which it is drawn.

Angle

The union of two rays that have the same end point.

Angle bisector

A line or any part of a line that contains the vertex of an angle and that divides the angle into two congruent angles. An angle has exactly one _____. (two words)

Angle of depression

An angle formed by a horizontal ray of sight and the ray that is the line of sight to an object below the horizontal ray. hint: (_) of (_) (three words)

Angle of elevation

An angle formed by a horizontal ray of sight and the ray that is the line of sight to an object above the horizontal ray. hint: (_) of (_) (three words)

Apothem

For a regular polygon, the radius of its inscribed circle.

Arc of a chord

The minor arc of a circle whose end points are the end points of the [chord]. If the chord is a diameter, then either semicircle is an arc of the diameter. hint: (_) of a (_) (four words)

Area

For a plane geometric figure, the number of square units it contains.

ASA Theorem of Congruence

Two triangles are congruent if two pairs of corresponding angles are congruent and the sides included by these angles are congruent. hint: ASA (_) of (_) (four words)

axiom

an accepted general truth or principle by virtue of a claim to intrinsic merit or on the basis of an appeal to self-evidence; a priori.

Base angles

The congruent [angles] that lie opposite the congruent sides of an isosceles triangle. (two words, plural)

Base

The noncongruent side of the isosceles triangle.

Bases

The parallel sides of a trapezoid. (plural)

Betweenness of points

A term that refers to the order of three collinear [points]. If A, B, and C are three different collinear points, point C is between points A and B if AC + CB = AB. hint: (_) of (_) (three words)

Bisect

To divide into two equal parts.

Center of a regular polygon

The common center of the inscribed circle and the circumscribed circle of a [regular polygon]. hint: (_) of a (_) (_) (six words)

Central angle

An [angle] whose vertex is at the center of a circle and whose sides are radii. (two words)

Central angle

An [angle] whose vertex is the center of the regular polygon and whose sides terminate at consecutive vertices of the polygon. (two words)

Centroid

The point at which the three medians of the triangle intersect.

Chord

A segment whose end points are on the circle.

Circle

The set of all points in a plane at a fixed distance from a given point called the center. The fixed distance is called the radius of the _____. An equation of a(n) _____ with center at point (h, k) and radius length r is r^2 = (x - h)^2 + (y - k)^2.

Circumference

The distance around the circle.

Circumscribed circle

A [circle] that passes through each vertex of a polygon. (two words)

Circumscribed polygon

A [polygon] that has all of its sides tangent to a circle. (two words)

Collinear points

[Points] that lie on the same line. (two words, plural)

Complementary angles

Two [angles] whose measures add up to 90. (two words, plural)

Concentric circles

[Circles] in the same plane that have the same center but have radii of different lengths. (two words, plural)

congruence

means 'same size' and 'same shape'

Congruent angles

[Angles] that have the same measure. (two words, plural)

Congruent circles

[Circles] with congruent radii. (two words, plural)

Congruent line segments

[Line segments] that have the same length. (three words, plural)

Congruent polygons

[Polygons] with the same number of sides that have the same size and the same shape. (two words, plural)

Congruent triangles

[Triangles] whose vertices can be paired so that any one of the following conditions is true: (1) the sides of one triangle are congruent to the corresponding sides of the other triangle (SSS con. SSS); (2) two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle (SAS con. SAS); (3) two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle (ASA con. ASA); (4) two angles and the side opposite one of these angles of one triangle are congruent to the corresponding parts of the other triangle (AAS con. AAS). Two right triangles are congruent if the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of the other triangle (Hy-Leg con. Hy-Leg). (two words, plural)

Congruent triangles

[Triangles] whose vertices can be paired so that the sides of one triangle are congruent to the corresponding sides of the other triangle (SSS con. SSS). (two words, plural)

Congruent triangles

[Triangles] whose vertices can be paired so that two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle (SAS con. SAS). (two words, plural)

Congruent triangles

[Triangles] whose vertices can be paired so that two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle (ASA con. ASA). (two words, plural)

Congruent triangles

[Triangles] whose vertices can be paired so that two angles and the side opposite one of these angles of one triangle are congruent to the corresponding parts of the other triangle (AAS con. AAS). (two words, plural)

Congruent triangles

Two right [triangles] where the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of the other triangle (Hy-Leg con. Hy-Leg). (two words, plural)

consecutive

adj.; following in a series, one right after the other

Converse of a conditional statement

Another [conditional statement] formed by interchanging the hypothesis ('Given') with the conclusion ('To Prove') of the original statement. hint: (_) of a (_) (_) (five words)

Convex polygon

A [polygon] each of whose interior angles measures less than 180. (two words)

Coordinate plane

A [plane] that is divided into four equal regions, called quadrants, by a horizontal number line and a vertical number line, called axes, intersecting at their zero points, called the origin. Each point in a _____ is located by an ordered pair of numbers of the form (x, y). The first member, x, of the ordered pair gives the directed distance of the point from the zero point of the x-axis (horizontal). The second member, y, of the ordered pair gives the directed distance of the point from the zero point of the y-axis. (two words)

Corollary

A theorem that can be easily proved by means of a closely related theorem.

Corresponding angles

Pairs of [angles] formed when a transversal intersects two lines. The two angles in each pair lie on the same side of the transversal, one angle per intersected line, but one angle is between the two lines (interior) and the other angle is exterior to the two lines. (two words, plural)

Cosine

For a right triangle, the ratio of the length of the leg that is adjacent to the acute angle to the length of the hypotenuse.

Decagon

A polygon with 10 sides.

Deductive reasoning

A step-by-step process by which a set of accepted facts is used to arrive at a conclusion. (two words)

Degree

A unit of angle measure. One _____ is the measure of an angle formed by 1/360 of one complete rotation of a ray about its end point.

Diagonal

A line segment whose end points are nonconsecutive vertices of the polygon.

Diameter

A chord of the circle that contains the center of the circle.

Distance formula

A [formula] used to find the length of the segment determined by two points in the coordinate plane. The distance d between two points A(xA, yA) and B(xB, yB) is given by the formula d = square root[(xB-xA)^2+(yB-yA)^2] (two words)

Dodecagon

A polygon with 12 sides.

Equiangular polygon

A [polygon] in which all of the angles have the same measure. (two words)

Equiangular triangle

A [triangle] in which all three angles have the same measure. (two words)

Equidistant

Means having the same distance.

Equilateral polygon

A [polygon] in which all of the sides have the same length. (two words)

Equilateral triangle

A [triangle] whose three sides have the same length. (two words)

Exterior angle

An [angle] formed by a side of the polygon and the extension of an adjacent side of the polygon. (two words)

Extremes

The first and fourth terms of a proportion. In the proportion a/b = c/d, a and d are the _____. (plural)

Half-plane

The set of points in a plane that lie on one side of a line. (two words, hyphenated)

Hexagon

A polygon with six sides.

Hypotenuse

The side of a right triangle that is opposite the right angle.

Incenter

The point at which the three angle bisectors of the triangle intersect.

Indirect proof

A method of [proof] in which each possibility except the one that needs to be proved is eliminated by showing that it contradicts some known or given fact. (two words)

Inscribed angle

An [angle] whose vertex lies on the circle and whose sides are chords of the circle. (two words)

Inscribed circle

A [circle] that is tangent to each side of a polygon. (two words)

Inscribed polygon

A [polygon] that has all of its vertices on a circle. (two words)

Isosceles trapezoid

A [trapezoid] whose nonparallel sides, called legs, have the same length. (two words)

Isosceles triangle

A [triangle] with two sides, called legs, that have the same length. (two words)

Leg

Either of the two sides of the right triangle that are not opposite the right angle.

Legs

The nonparallel sides of a trapezoid. (plural)

Line

A term undefined in geometry; a _____ can be described as a continuous set of points forming a straight path that extends indefinitely in two opposite directions.

Line segment

Part of a line that consists of two different points on the line, called end points, and the set of all points on the line that are between them. (two words)

Locus

The set of all points, and only those points, that satisfy a given condition.

Major arc

An [arc] of a circle whose degree measure is greater than 180. (two words)

Means

The two middle terms of a proportion. In the proportion A/B = C/D ,the terms B and C are the _____. If B = C, then either B or C is called the _____(singular) proportional between A and D, which are called the extremes. (plural)

Median

A line segment whose end points are the midpoints of the legs of the trapezoid.

Median

A line segment whose end points are a vertex of the triangle and the midpoint of the side opposite that vertex.

Midpoint formula

A [formula] used to find the coordinates of the midpoint of a line segment in the coordinate plane. (two words)

Midpoint

The point on the line segment that divides the segment into two segments that have the same length.

Minor arc

An [arc] of a circle whose degree measure is less than 180. (two words)

Obtuse angle

An [angle] whose degree measure is greater than 90 and less than 180. (two words)

Obtuse triangle

A [triangle] that contains an obtuse angle. (two words)

Octagon

A polygon with eight sides.

Opposite rays

Two [rays] that have the same end point and form a line. (two words, plural)

Ordinate

The y-coordinate of a point in the coordinate plane.

Origin

The zero point on a number line.

Orthocenter

The point at which the three altitudes of the triangle intersect.

Parallel lines

[Lines] in the same plane that do not intersect. (two words, plural)

Parallelogram

A quadrilateral that has two pairs of parallel sides.

Pentagon

A polygon with five sides.

Perimeter

The sum of the lengths of the sides of the polygon.

Perpendicular bisector

A line, ray, or line segment that is perpendicular to a segment at its midpoint. (two words)

Perpendicular lines

Two [lines] that intersect at a 90-degree angle. (two words, plural)

Plane

A term undefined in geometry; a(n) _____ can be described as a flat surface that extends indefinitely in all directions.

Point

A term undefined in geometry; a line with no size that indicates location.

Polygon

A closed figure in a plane whose sides are line segments that intersect at their end points.

Postulate

A statement whose truth is accepted without proof; assumed to be true.

Proportion

An equation that states that two ratios are equal. In a _____ the product of the means equals the product of the extremes. Hence, if a/b = c/d, then b X c = a X d.

Pythagorean theorem

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. (two words)

Quadrant

One of the four equal rectangular regions into which a coordinate plane is divided.

Quadrilateral

A polygon with four sides.

Radius

A line segment whose end points are the center of the circle and any point on the circle.

Ratio

A comparison of two numbers by division. The _____ of a to b can be represented by the fraction a/b, provided that b != 0.

Ratio of similitude

The constant [ratio] of the lengths of any two corresponding sides of two similar polygons. hint: (_) of (_) (three words)

Ray

The part of a line that consists of a fixed point, called an end point, and the set of all points on one side of the end point.

Reciprocal

The number that, when multiplied by an original nonzero number, gives 1. For example, the _____ of 5 is 1/5 since 5 x 1/5 = 1.

Rectangle

A parallelogram with four right angles.

Regular polygon

A [polygon] that is both equiangular and equilateral. (two words)

Rhombus

A parallelogram with four sides that have the same length.

Right angle

An [angle] whose degree measure is 90. (two words)

Right triangle

A [triangle] that contains a right angle. (two words)

SAS Theorem of Congruence

Two triangles are congruent if two pairs of corresponding sides are congruent and the angles formed by these sides are congruent. hint: SAS (_) of (_) (four words)

Scalene triangle

A [triangle] in which no two sides have the same length. (two words)

Secant

A line that intersect a circle in two different points.

Semicircle

An arc whose end points are a diameter of the circle.

Similar polygons

[Polygons] that have the same shape but may have different sizes. Two polygons with the same number of sides are _____ if corresponding angles are congruent and the lengths of corresponding sides are in proportion. (two words, plural)

Sine

For a right triangle, the ratio of the length of the leg that is opposite the acute angle to the length of the hypotenuse.

Slope

A numerical measure of the steepness of a nonvertical line.

Slope

The _____ of a line is the difference of the y-coordinates of any two different points on the line divided by the difference of the corresponding x-coordinates of the two points.

Slope

The _____ of a horizontal line is 0, and the _____ of a vertical line is not defined.

Slope formula

A [formula] used to calculate the slope of a nonvertical line when the coordinates of two points on the line are given. (two words)

Slope-intercept form

An equation that has the [form] y = mx + b, where m is the slope of a non-vertical line and b is the y-coordinate of the point at which the line crosses the y-axis. (three words, first two hyphenated)

Square

A rectangle all of whose sides have the same length.

SSS Theorem of Congruence

Two triangles are congruent if three pairs of corresponding sides are congruent. hint: SSS (_) of (_) (four words)

Supplementary angles

Two [angles] whose measures add up to 180. (two words, plural)

Tangent

For a right triangle, the ratio of the length of the leg that is opposite a given acute angle to the length of the leg that is adjacent to the same angle.

Tangent

A line that intersects a circle in exactly one point, called the point of tangency.

point of tangency

The point at which a line intersects a circle in exactly one point. hint: (_) of (_) (three words)

Theorem

A generalization that can be proved.

Transversal

A line that intersects two lines at different points.

Trapezoid

A quadrilateral with exactly one pair of parallel sides.

Triangle

A polygon with three sides.

Undefined term

A [term] that can be described but is so basic that it cannot be defined. The terms point, line, and plane are _____s in geometry. (two words)

Vertex

The point at which two sides of a polygon intersect.

Vertices

The plural of vertex.

Vertex angle

The [angle] formed by the congruent sides of an isosceles triangle. (two words)

Vertical angles

Pairs of nonadjacent (opposite) [angles] formed by two intersecting lines. (two words, plural)

Volume

The capacity of a solid figure as measured by the number of cubic units it contains.

x-axis

The horizontal number line in the coordinate plane. (hyphenated)

x-coordinate

The first number in the ordered pair that represents the coordinates of a point in the coordinate plane. The _____ gives the directed horizontal distance of the point from the origin. (hyphenated)

y-axis

The vertical number line in the coordinate plane. (hyphenated)

y-coordinate

The second number in the ordered pair that represents the coordinates of a point in the coordinate plane. The _____ gives the directed vertical distance of the point from the origin. (hyphenated)

y-intercept

The y-coordinate of the point at which a nonvertical line crosses the y-axis. (hyphenated)