Elementary geometry

one-dimensional infinite non-curved geometric object

A sphere (from Ancient Greek , ) is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance from a given point in three-dimensional space. That given point is the center of the sphere, and the distance is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians.

[[File:Circle-withsegments.svg|thumb|right|Circle with

mathematical system attributed to Euclid

thumb|250px|Perimeter is the distance around a two-dimensional [[shape, the length of the shape's boundary.]]

part of a line that is bounded by two distinct end points; line with two endpoints

thumb|A children's toy called Shape-O, made by Tupperware Brands|Tupperware, used for learning various shapes.

thumb|right|The diagonals of a cube with side length 1. AC' (shown in blue) is a [[space diagonal with length \sqrt 3, while AC (shown in red) is a face diagonal and has length \sqrt 2.]] thumb|Horizontal (left), vertical (center) and diagonal (right) double arrows.

220px|right|thumb|Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot. 220px|right|thumb|Tangent plane to a sphere

intersection of the sphere and a plane which passes through the center point of the sphere

relation used in geometry

line segment joining two adjacent vertices in a polygon or polytope

thumb|Estimating the height of a mountain using triangulation

axiom in Euclidean geometry

angular measurement describing how large a sphere or circle appears from a given point of view

set of points whose location satisfies or is determined by one or more specified conditions

middle point, in some sense, of an object in geometry

in Euclidean geometry, a function that moves every point a constant distance in a specified direction

geometric surface defined by two concentric circles

intersection of a body in 3D space with a plane

in geometry, a planar surface that forms part of the boundary of a solid object

Rectangle with side lengths in the golden ratio

measure of two radii meeting

282px|thumb|The midpoint of the segment (1, 1) to (2, 2)

In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180° (equivalently, radians, or a half-turn). It only has one line of symmetry (reflection symmetry).

lines in 3D that do not intersect and neither do they point the same direction

(in a plane mirror) reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface

term in geometry

two segments that divide a triangle

line determined by two circles

a family of circles where every one intersects every circle in a second family of circles orthogonally

theorem

sphere contained within a polyhedron, tangent to each of its faces

line that passes through two lines in the same plane at two distinct points

symmetry with respect to a plane, when the shape does not change by reflecting all of its part from a mirror plane

in geometry, multiple lines or curves intersecting at a single point

right|thumb|Line DE bisects line AB at D, line EF is a perpendicular bisector of segment AD at C, and line EF is the interior bisector of right angle AED.

a set of points that lie on a single circle

sphere that contains a polyhedron and touches each of the vertices thereof

triangle defined from the midpoints of the sides of another triangle

line segment connecting opposite polyhedron vertices

inequality of sum of squares of sides of triangle

navigation based on the measurement of the distances to two stations at known locations

notation used to describe polyhedra based on a seed polyhedron modified by various operations

thumb|100px|right

describes a property of the cevians of a triangle intersecting in a common point

tangential and cyclic polygon

line antiparallel to another one

Region between two concentric spheres of differing radii

Mathematical question

type of region of the Cartesian plane

intersection point of the three radical axes of the pairs of circles

geometric figure which is "snugly enclosed" by another figure

In geometry, a generatrix () or describent is a point, curve or surface that, when moved along a given path, generates a new shape. The path directing the motion of the generatrix motion is called a directrix or dirigent.

right|thumb|Perpendicular bisector of a line segment. The point where the red line crosses the black line segment is equidistant from the two end points of the black line segment. thumb|The cyclic polygon P is circumscribed by the circle C. The circumcentre O is equidistant to each point on the circle, and a fortiori to each vertex of the polygon.

Given a triangle and a point, constructs a second triangle with a special point

circle formed from an arbelos, orthogonal to two of the semicircles of the arbelos and to a tangent circle within it

geometry theorem relating to triangles

postulates of Euclidean geometry