A Geometer’s Glossary

Note: The definitions contained in this glossary were obtained either from our text (A Problem Solving Approach to Mathematics for Elementary School Teacher, Sixth Edition) OR from Dr. Rivera’s memory.

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

W

X

Y

Z