# Geometry's Glossar

## A

Acute angle – an angle measuring less than 90 degrees
Acute triangle – a triangle with exactly 3 acute angles
Adjacent angles – angles that share a common vertex and a common side and have nonoverlapping interiors
Alternate exterior angles – a pair of exterior angles that are on different sides of the transversal and are not supplementary
Alternate interior angles – a pair of interior angles that are on different sides of the transversal and are not supplementary
Altitude of a triangle – a perpendicular segment which connects a vertex of the triangle to the line containing the opposite side from the vertex
Angle – formed by two rays which share a common endpoint
Apex – the point of a pyramid
Arc – any part of a circle that can be drawn without lifting your pencil
Area – the number of square units required to cover a region with no gaps or overlaps

## B

Base – the upper and lower parallel faces of a prism
Bisect – to divide into two congruent pieces

## C

Center of an arc – the center of a circle containing the arc
Circle – the set of all points in a plane that lie the same distance from a given point (the center)
Circular cone/cylinder – a cone/cylinder whose base(s) are circular regions
Circumference – the perimeter of a circle
Collinear – points that lie in the same line
Complementary angles – a pair of angles whose measures sum to 90 degrees
Concave polygons – a polygon in which it is possible to draw a segment between two points of the polygonal region such that part of the segment lies outside of the region (it has “caves”)
Concurrent lines – lines that contain the same point; may be coplanar or noncoplanar
Cone – a simple-closed surface with one base which is a simple-closed curve (other than a polygon) which is connected by line segments to a point off the curve
Congruent – two objects are congruent if they have the same size and the same shape
Convex polygon – a polygon in which it is impossible to draw a segment between two points of the polygonal region such that part of the segment lies outside of the region (it does not have “caves”)
Coplanar – points (or lines) that lie in the same plane
Corresponding angles – a pair of angles that are in the same “position” relative to the two figures to which they belong
Cube – a regular polyhedron with 6 square-shaped sides
Cylinder – a simple-closed surface with two congruent, parallel bases which are simple-closed curves (other than a polygon)

D

Decagon – a polygon with 10 sides
Diagonal – a segment drawn within a polygon whose endpoints are non-consecutive vertices of the polygon
Dihedral angle – the union of two half-planes; ex. The union of the wall and the floor of our classroom
Dodecagon – a polygon with 12 sides
Dodecahedron – a regular polyhedron with 12 pentagon-shaped sides

E

Equilateral triangle – a triangle in which all three sides have the same measure
Exterior angle – an angle which does not lie between two parallel lines and is formed by one of the lines and a transversal
Exterior angle of a polygon – an angle formed by a side of the polygon and the extension of a contiguous side of the polygon

F

Faces – the polygonal regions of a polyhedron
Flip – see reflection

G

Glide reflection – a motion which combines a translation and a reflection

H

Half-turn – a rotation of 180 degrees
Heptagon – a polygon with 7 sides
Hexagon – a polygon with 6 sides
Hypotenuse – in a right triangle, the leg opposite the right angle

I

Icosahedron – a regular polyhedron with 20 triangle-shaped sides
Interior angle – an angle which lies between two parallel lines and is formed by one of the lines and a transversal
Interior angle of a polygon – an angle formed within a polygon by two sides of the polygon sharing a common vertex
Intersecting lines – two coplanar lines that have exactly one point in common
Isometry – any motion that preserves distance; also called rigid motion
Isosceles trapezoid – a trapezoid in which the two non-parallel sides are congruent
Isosceles triangle – a triangle in which at least two sides have the same length

J

K

Kite – a quadrilateral with at least two distinct pairs of consecutive sides congruent

L

Lateral faces – the faces other than bases of a prism
Line of symmetry – a figure has a line of symmetry if it is its own image under a reflection in the line; if you fold the figure along the line of symmetry it falls on top of itself

M

Major arc – an arc which is larger than a semicircle
Minor arc – an arc which is smaller than a semicircle

N

Net – a two-dimensional pattern that can be used to construct a three-dimensional figure
Nonagon – a polygon with 9 sides

O

Oblique cylinder/cone – a “leaning” cylinder
Oblique prism – a prism which has faces that are not all bounded by rectangles; a prism which “leans”
Obtuse angle – an angle which measures greater than 90 degrees
Obtuse triangle – a triangle with exactly one obtuse angle
Octagon – a polygon with 8 sides
Octahedron – a regular polyhedron with 8 triangle-shaped sides

P

Parallel lines – two distinct coplanar lines that have no points in common
Parallelogram – a quadrilateral in which each pair of opposite sides is parallel
Pentagon – a polygon with 5 sides
Perimeter – the distance around a figure
Perpendicular bisector – a line which is perpendicular to a segment and it bisects the segment
Perpendicular lines – two lines which intersect to form right angles
Pi – the ratio of the circumference of a circle to its diameter; typically we use 3.14 or 22/7 as an approximation of pi
Plane of symmetry – a three-dimensional figure has a plane of symmetry when every point of the figure on one side of the plane has a mirror image on the other side of the plane
Point symmetry – any figure that has 180 degree rotational symmetry is said to have point symmetry about the turn center
Polygon – a simple, closed polygonal curve
Polyhedron – a simple closed surface made up of polygonal regions
Prism – a polyhedron in which the two congruent bases lie in parallel planes and the other faces are bounded by parallelograms
Pyramid – a polyhedron with one base and lateral faces which are triangles that come together at a point

Q

Quadrilateral – a polygon with 4 sides

R

Rectangle – a parallelogram with four right angles
Reflection – also called a flip; a motion which pairs each point of a figure with a corresponding point in a new figure in such a way that each line connecting the pairs of points is perpendicular to the line of reflection
Regular polygon – a polygon in which all sides are congruent and all interior angles are congruent
Regular polyhedron – a convex polyhedron whose faces are congruent regular polygonal regions such that the number of edges that meet at each vertex is the same for all of the vertices of the polyhedron
Regular tessellation – a tessellation which involves copies of a regular polygon
Rhombus – a parallelogram with all four sides congruent
Right angle – an angle which measures exactly 90 degrees
Right cylinder/cone – a cylinder/cone which does not “lean”
Right prism – a prism whose lateral faces are rectangles; a prism that is not “leaning”
Right triangle – a triangle with exactly one right angle
Rigid motion – see isometry
Rotation – a motion determined by holding one point – the center – fixed and rotating the figure about this point by a certain amount in a certain direction; also called a turn
Rotational symmetry – also called turn symmetry; when a figure can be rotated about some point less than 360 degrees and the figure falls on top of itself

S

Scale factor – the ration of the corresponding sides in similar figures
Scalene triangle – a triangle in which all three sides have different lengths
Semicircle – an arc which is half of a circle; an arc whose central angle is 180 degrees
Similar – two objects are similar if they have the same shaped but not necessarilty the same size
Simple closed surface – has exactly one interior, has no holes, and is hollow
Size transformation – a transformation which creates a figure similar to the original figure
Skew lines – two lines which cannot lie in the same plane (they do not intersect but they are not parallel either since they are in different planes)
Slide – see translation
Sphere – the set of all points in space that are a given distance from a given point (the center); it looks like a ball
Square – a rectangle with 4 congruent sides
Straight angle – an angle which measure exactly 180 degrees
Supplementary angles – a pair of angles whose measures sum to 180 degrees

T

Tessellation – covering a plane with copies of a figure in such a way that there are no gaps and no overlaps
Tetrahedron – a regular polyhedron with 4 triangle-shaped sides
Translation – also called a slide; a motion that involves moving every point of a figure a specified distance and a specified direction along a straight line
Transversal – a line that intersects a pair of lines
Trapezoid – a quadrilateral with exactly one pair of parallel sides
Triangle – a polygon with 3 sides
Turn – see rotation
Turn symmetry – see rotational symmetry

U

V

Vertex – the point of a cone
Vertical angles – a pair of angles which lie across from each other when two lines intersect

Keywords: geometry, words, geometrical words

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