CHAPTER 10 VOCAB

Symmetry

A figure has ____________ if there exists a rigid motion- reflection, translation, rotation or glide reflection- that maps the figure onto itself.

Line symmetry

________________ occurs when a figure can be mapped onto itself by a reflection in a line.

Line of symmetry

A line that can be drawn through a plane figure so that the figure on one side is the reflection image of the figure on the opposite side.

Rotational symmetry

If a figure can be rotated less than 360 degrees about a point so that the image and the preimage are indistinguishable, then the figure has rotational symmetry.

Center of symmetry

the point in the center of a figure about which the figure can be mapped onto itself by a rotation

Order of symmetry

The number of times a figure can map onto itself as it rotates from 0 degrees to 360 degrees

Magnitude of symmetry

The smallest angle through which a figure can be mapped so that it maps onto itself.

Plane symmetry

A three dimensional figure has ______________ if the figure can be mapped onto itself by a reflection in a plane.

Axis symmetry

A three dimensional figure has _____________ if the figure can be mapped onto itself by a rotation between 0 and 360 degrees in a line called _____________.

Point symmetry

____________ is when every part has a matching part, the same distance from the central point, but in the opposite direction.

circle

The set of all points in a plane equidistant from a given point.

center

The point on the plane containing a circle from which all points of the circle are equidistant.

radius

A segment with endpoints at the center and on the circle.

chord

A segment with endpoints on the circle.

diameter

A chord that passes through the center and made up of colinear radii.

concentric circles

Coplanar circles that have the same center.

circumference

The distance around a circle.

Pi

An irrational number equal to the ratio of the circumference to the diameter.

Inscribed

A polygon whose vertices all lie on the circle.

circumscribed

A circle containing all of the vertices of a polygon.

Central angle

an angle with its vertex at the center of a circle

arc

a portion of a circle defined by two endpoints

Minor arc

the shortest arc connecting two endpoints on a circle

Major arc

The longest arc connecting two endpoints on a circle.

Semicircle

An arc of a circle whose endpoints lie on a diameter

congruent arcs

arcs in the same or congruent circles that have the same measure

adjacent arcs

arcs in a circle that have exactly one point in common

arc length

the distance between the endpoints along an arc measured in linear units

Inscribed angle

an angle that has a vertex on a circle and sides that contain chords of the circle

Intercepted arc

An angle intercepts an arc if and only if each of the following conditions are met.

The endpoints of the arc lie on the angle.

All points of the arc except the endpoints are in the interior of the circle.

Each side of the angle has an endpoint of the arc.

Tangent

A line in the plane of a circle that intersects the circle in exactly one point.

point of tangency

The point at which a tangent line intersects a circle

Common tangent

A line or segment that is tangent to two circles in the same place

Secant

Any line that intersects a circle in exactly two points

Chord segment

when two chords intersect inside a circle, each chord is divided into two segments called ___________.

Secant segment

A(n) _____ is a segment of a secant line with exactly one endpoint on the circle.

External secant segment

a secant segment that lies in the exterior of the circle

Tangent segment

A(n) _____ is a segment of a tangent with one endpoint on the circle.

Compound Locus

A _________________ problem involves two or more locus conditions occurring at the same line. The different conditions in a _______ problem are generally separated by the words "AND" or "AND ALSO".