Geometry Terms

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Definitions of terms to know as we encounter them in the text. Make sure you can draw them and know the symbols to indicate them.

reflectional symmetry

when you can fold a design along a line of symmetry so that all points on one side of the line exactly match all the points on the other side. Also called line or mirror symmetry.

rotational symmetry

when a design looks the same after you turn it around a point by less than a full circle. The # of times it looks the same as you turn it a full 360 degrees determines the type (3-fold, 5-fold etc.)

bilateral symmetry

when an object has just one line of reflectional symmetry. (butterfly or human body etc.)

line

a straight , continuous arrangement of infinitely many points, with infinite length but no thickness, extending forever in two directions. Named by giving the letter names of any two points on the line and by placing the line symbol above the letters.

plane

has infinite length and infinite width, but no thickness. Named with a script capital letter.

collinear

on the same line.

coplanar

on the same plane.

line segment

a set of points on a line consisting of two endpoints and all the points between them.

congruent segments

line segments that have the same length.

midpoint

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

bisect

the midpoint bisects the segment,or divides the segment into two congruent segments.

ray

a straight line extending from a point.

Coordinate Midpoint Property

if (x1, y1) and (x2, y2) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are (x1+x2/2, y1+y2/2)

angle

formed by two rays that share a common endpoint, provided that the two rays are noncollinear.

vertex

the common endpoint of the two rays of an angle.

sides of an angle

the two rays of an angle

measure of an angle

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

congruent angles

if and only if two angles have the same measure. You use identical markings to show on a figure.

angle bisector

a ray is the angle bisector if it contains the vertex and divides the angle into two congruent angles.

incoming angle (in pool)

is formed by the cushion and the path of the ball approaching the cushion.

outgoing angle (in pool)

is formed by the cushion and the path of the ball leaving the cushion.

Steps to creating a good definition

1. Classify your term. What is it?
2. Differentiate your term. How does it differ from others in that class?
3. Test your definition by looking for a counterexample.

right angle

an angle that measures exactly 90 degrees

acute angle

an angle that measures less than 90 degrees.

obtuse angle

an angle that measures more than 90 degrees but less than 180 degrees

Pair of vertical angles

angles formed by two intersecting lines; they share a common vertex but not a common side

Pair of linear angles

two supplementary adjacent angles formed by 2 intersecting lines ; they share a vertex and a side

Pair of Supplementary angles

two angles whose measures have a sum of 180 degrees

Pair of Complementary angles

two angles that have the sum of 90 degrees.

Polygon

a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others. Each line segment is called a side of the polygon and each endpoint where the sides meet is called a vertex.

Diagonal of a polygon

a line segment that connects two nonconsecutive vertices.

Convex polygon

if no diagonal of a polygon is outside the polygon.

Concave polygon

if at least one diagonal of the polygon is outside the polygon.

Congruent polygons

if and only if polygons are exactly the same size and shape.

Equilateral polygon

all the sides of a polygon have equal length.

Equiangular polygon

all the angles have equal measure.

Regular polygon

is both equilateral and equiangular

Right triangle

a triangle with one right angle.

Acute triangle

a triangle with 3 acute angles (less than 90 degrees)

Obtuse triangle

a triangle where one angle is obtuse (measures over 90 degrees).

Scalene triangle

a triangle that has no congruent sides.

Equilateral triangle

a triangle with three congruent sides.

Isosceles triangle

a triangle with at least 2 congruent sides.

Trapezoid

a quadrilateral with exactly one pair of parallel sides.

Parallelogram

a quadrilateral with 2 pairs of parallel sides

Rhombus

an equilateral parallelogram.

Rectangle

a parallelogram with four right angles

Square

an equilateral rectangle.

Circle

the set of all points in a plane at a given distance (radius) from a given point (center) in the plane. Has an arc measure of 360 degrees.

Radius

a segment from the center to a point on the edge of the circle. It's length is also called the radius.

Diameter

a line segment containing the center, with its endpoints on the circle. The length of this segment is also called the diameter.

Congruent circles

two or more circles that have the same radius.

Concentric circles

two or more coplanar circles that share the same center.

Arc of a circle

two points on the circle and the continuous (unbroken) part of teh circle between the two points. The two points are called the endpoints of the arc.

Semicircle

an arc of a circle whose endpoints are the endpoints of a diameter. It has an arc measure of 180 degrees.

Minor arc

an arc of a circle that is smaller than a semicircle.

Major arc

an arc of a circle that is larger than a semicircle.

Central angle of a circle

the angle with its vertex at the center of the circle, and sides passing through the endpoints of the arc.

Chord

line segment whose endpoints are any two points on a circle

Tangent

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

Prism

A solid figure that has two congruent, parallel polygons as its bases. Its sides are parallelograms

Pyramid

a solid figure with a polygon base and triangular sides that meet at a single point

Cylinder

a 3-dimensional figure that has 2 congruent circular faces (soup can)

Cone

a shape whose base is a circle and whose sides taper up to a point

Sphere

a three-dimensional closed surface such that every point on the surface is equidistant from the center

Hemisphere

half of a sphere

Space

the set of all points.

Isometric drawing

a 2-D drawing of an 3-D object, in which 3 sides of the object are shown from a corner view.

Inductive reasoning

the process of observing data, recognizing patterns, and making generalizations about those patterns.

Conjecture

a generalization made from inductive reasoning.

Deductive reasoning

the process of showing that certain statements follow logically from agreed-upon assumptions and proven facts. Involves logical and orderly reasoning from accepted truths.

Function rule

the rule that gives the nth term for a sequence.

Linear function

rules that generate a sequence with a constant difference. In the form f(n)=mx+b, where: f(n) is the value (y) or dependant variable; x is the term# or independant variable, m is the constant difference (coefficient, slope) and b is the y-intercept.

Segment bisector

a line, rar, or segment in a plane that passes through the midpoint of a segment in a plane.

Perpendicular bisector

The one segment in a plane that is also perpendicular to the segment.

Median of a triangle

the segment connecting the vertex of a triangle to the midpoint of its opposite side.

Midsegment of a triangle

the segment that connects the midpoints of two sides of a triangle.

Distance from a point to a line

is the length of the perpendicular segment from the point to the line.

Altitude of a triangle

a perpendicular segment from a vertex to the opposite side or to a line containing the opposite side. It may be inside the triangle, outside the triangle or one of its sides. The length of the altitude is the height of the triangle. Every triangle has three.

Concurrent

when three or more lines have a point in common. The point of intersection of segments, rays, planes or lines is called "the point of concurrency"

Incenter

The point of concurrency for the three angle bisectors of a triangle.

Circumcenter

The point of concurrency for the perpendicular bisectors of a triangle.

Orthocenter

The point of concurrency for the three altitudes of a triangle.

Centroid

The point of concurrency for the three medians of a triangle.

Auxilary line

An extra line added to help with a proof.

Parts of a triangle

in a diagram, know which is: the vertex angle, the base angles, the legs and the base.

CPCTC

an abbreviation for the definition of congruent triangles which states that "corresponding parts of congruent triangles are congruent." This can be used in proofs.

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