# Geometry 1.1-1.7

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Vocabulary from Discovering Geometry sections 1.1 thru 1.7

### point

An undefined term thought of as a location with no size or dimension. It is the most basic building block of geometry. In a two-dimensional coordinate system, its location is represented by an ordered pair of numbers (x, y).

### line

An undefined term thought of as a straight, continuous arrangement of infinitely many points extending forever in two directions. It has length, but no width or thickness, so it is one-dimensional.

### plane

An undefined term thought of as a flat surface that extends infinitely along its edges. It has length and width but no thickness, so it is two-dimensional.

### definition

A statement that clarifies or explains the meaning of a word or phrase.

### collinear

On the same line.

### coplanar

In the same plane.

### line segment

Two points and all the points between them that are collinear with the two points.

### endpoint

The point at either end of a segment or arc, or the first point of a ray.

### congruent segments

Two or more segments that have the same measure or length.

### midpoint

The point on a line segment that is the same distance from both endpoints.

### Midpoint Formula

The midpoint between (x1,y1) and (x2,y2) is found by using ( (x1+x2)/2 , (y1+y2)/2 )

### bisect

To divide into two congruent parts.

### ray

A point on a line, and all the points of the line that lie on one side of this point.

### angle

Two non-collinear rays having a common endpoint

### vertex (of an angle)

The common endpoint of the two rays of the angle.

### side (of an angle)

One of the two rays that form an angle.

### measure of an angle

The smallest amount of rotation about the vertex from one ray to the other, measured in degrees.

### degree

A unit of measure for angles and arcs equivalent to 1/360 of a rotation around a circle.

### protractor (or geometer)

A tool used to measure the size of an angle in degrees.

### congruent angles

Two or more angles that have the same measure.

### angle bisector

A ray that has its endpoint at the vertex of the angle and that divides the angle into two congruent angles.

Two non-overlapping angles with a common vertex and one common side.

### counterexample

An example that shows a conjecture to be incorrect or a definition to be inadequate.

### perpendicular

Lines that meet at 90° angles.

### parallel

Lines that lie in the same plane and do not intersect.

### skew lines

Lines that are not in the same plane and do not intersect.

### right angle

An angle whose measure is 90°.

### acute angle

An angle whose measure is less than 90°.

### obtuse angle

An angle whose measure is greater than 90°, but less than 180°.

### complementary angles

Two angles whose measures have the sum 90°.

### supplementary angles

Two angles whose measures have the sum 180°.

### vertical angles

Two nonadjacent angles formed by two intersecting lines.

### linear pair (of angles)

Two adjacent supplementary angles whose non-common sides form a line.

### polygon

A closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others.

### side (of a polygon)

A line segment connecting consecutive vertices of a polygon.

### vertex (of a polygon)

An endpoint where two sides of the polygon meet.

### angle (of a polygon)

An angle having two adjacent sides of the polygon as its sides.

### triangle

A polygon with 3 sides

A polygon with 4 sides

### pentagon

A polygon with 5 sides

### hexagon

A polygon with 6 sides

### heptagon

A polygon with 7 sides

### octagon

A polygon with 8 sides

### nonagon

A polygon with 9 sides

### decagon

A polygon with 10 sides

### undecagon

A polygon with 11 sides

### dodecagon

A polygon with 12 sides

### n-gon

A polygon with n sides.

### consecutive (angles, sides or vertices of a polygon)

Two angles that share a common side, two sides that share a common vertex, or two vertices that are the endpoints of one side.

### diagonal

A line segment connecting two nonconsecutive vertices of a polygon or polyhedron.

### convex polygon

A polygon with no diagonal outside the polygon.

### concave polygon

A polygon with at least one diagonal outside the polygon.

### congruent polygons

Two or more polygons with the exact same size and shape.

### perimeter

The length of the boundary of a two-dimensional figure. For a polygon it is the sum of the lengths of its sides.

### equilateral polygon

A polygon whose sides are congruent.

### equiangular polygon

A polygon whose angles are congruent.

### regular polygon

A polygon that is both equilateral and equiangular.

### assume

To accept as true without facts or proof.

### right triangle

A triangle with a right angle.

### acute triangle

A triangle with three acute angles.

### obtuse triangle

A triangle with an obtuse angle.

### scalene triangle

A triangle with three sides of different lengths.

### equilateral triangle

A triangle whose sides are congruent.

### isosceles triangle

A triangle with at least two congruent sides. Note : Most have only two congruent sides, although an equilateral triangle can be considered one as well.

### vertex angle

The angle between the two congruent sides (of an isosceles triangle)

### base

The side opposite the vertex angle. (of an isosceles triangle)

### base angles

The two angles opposite the two congruent sides. (of an isosceles triangle)

### trapezoid

A quadrilateral with exactly one pair of parallel sides

### kite

A quadrilateral with exactly two distinct pairs of congruent consecutive sides.

### parallelogram

A quadrilateral in which both pairs of opposite sides are parallel.

### rhombus

An equilateral parallelogram.

### rectangle

An equiangular parallelogram.

### square

An equiangular rhombus, an equilateral rectangle, a regular quadrilateral.

### circle

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

### center (of a circle)

The coplanar point from which all points of the circle are the same distance.

A line segment from the center of a circle or sphere to a point on the circle or sphere. Also, the length of that line segment.

### chord

A line segment whose endpoints lie on a circle.

### diameter

A chord of a circle that contains the center, or the length of that chord.

### tangent line

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

### point of tangency

The point of intersection of a tangent line and a circle.

### congruent circles

Two or more circles with the same radius.

### concentric circles

Circles that share the same center.

### arc

Two points on a circle and the continuous part of the circle between them.

### semicircle

An arc of a circle whose endpoints are the endpoints of a diameter. An arc whose degree measure is 180°.

### minor arc

An arc of a circle that is less than a semicircle.

### major arc

An arc of a circle that is greater than a semicircle.

### arc measure

The measure of the central angle that intercepts an arc, measured in degrees.

### central angle

An angle whose vertex is the center of a circle and whose sides pass through the endpoints of an arc.

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