Point
An undefined term
Line
An undefined term
Plane
An undefined term
Definition
A statement that explains the meaning of a work or phrase
Collinear
Lying on the same line
Coplanar
Lying on the same plane
Line segment
End points and all the points in between them that are on the line segment containing them
Endpoints
The point at the ends of a line segment
Congruent Segments
Line segments that have the same length
Midpoint
The point on the line segment that is the same distance from both ends
Bisect
To cut into two equal parts
Ray
All points on a line that lie on one side of a specific point (the ray's endpoint)
Angle
Two non-collinear rays (the sides) having a common endpoint (the vertex)
Vertex (of an angle)
A point of intersection of two or more rays
Sides (of an angle)
The two rays having a common vertex that form an angle
Measure (of an angle)
The smallest amount of rotation necessary to rotate from one ray of the angle to the other (usually measured in degrees)
Degree
A unit of measure for angles and arcs equivalent to 1/360th of rotation around a circle
Protractor
A tool used to measure the size of an angle in degrees
Congruent angles
Angles that have the same measure
Angle bisector
A ray that has the vertex of the angle as it's endpoint and that divides the angle into two congruent parts
Incoming angle
The angle formed by the path of the approaching object and the surface it rebounds against
Outgoing angle
The angle formed by the path of the rebounding object and the surface it collided with
Classify
A part of a good definition that categorizes something according to some chosen characteristics
Differentiate
A part of a good definition that shows how it is different from other things defined
Counterexample
An example that shows that a conjecture is incorrect or a definition is inaccurate (definitions should be tested for these)
Parallel lines
Two lines that do NOT intersect
Perpendicular lines
Lines that meet at right angles
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 more than 90�
Pair of vertical angles
Two congruent angles formed by intersecting lines
Linear pair of angles
Two adjacent angles whose distinct sides lie on the same line
Pair of complementary angles
Two angles whose measures have a sum of 90�
Pair of supplementary angles
Two angles whose measures have a sum of 180�
Polygon
A closed planar geometric figure consisting of line segments each of which intersects exactly two other at endpoints forming the polygon's angles
Triangle
Three sides
Quadrilateral
Four sides
Pentagon
Five sides
Hexagon
Six sides
Heptagon
Seven sides
Octagon
Eight sides
Nonagon
Nine sides
Decagon
Ten sides
Undecagon
Eleven sides
Dodecagon
Twelve sides
n-gon
n-sides
Side (of polygon)
A line segment connecting two vertices
Vertex (of polygon)
A point of intersection of two or more line segments in a geometric figure
Consecutive angles (of a polygon)
Two angles that have a common vertex
Consecutive sides (of a polygon)
Two sides that have a common vertex
Diagonal
A line segment connecting two opposite vertices of a polygon or polyhedron
Convex polygon
A polygon having no diagonal lying outside the polygon
Concave polygon
A polygon having a diagonal lying outside the polygon
Congruent polygons
Two or more polygons that are identical in size and shape
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 with three congruent sides
Isosceles triangle
A triangle with at least two congruent sides
Vertex angles (of an isosceles triangle)
The angles between the congruent sides
Base (of a polygon)
A side of a polygon or face of a solid used as reference when drawing an altitude or other feature
Base angles (of an isosceles triangle)
The two angles opposite the two congruent sides
Trapezoid
A quadrilateral with exactly two distinct pairs of congruent consecutive sides
Parallelogram
A quadrilateral with the opposite sides parallel
Rhombus
An equilateral parallelogram
Rectangle
An equiangular parallelogram
Square
An equiangular rhombus or an equilateral rectangle
Locus
The set of all points in a plane satisfying a given condition; the path of a moving point
Tree diagram
A concept map in the form of a tree
Venn diagram
A circle diagram used to show relationships among members of different sets
Net
A two-dimensional pattern that you can cut our and fold to form a three-dimensional figure.
Transformation
Creating an image of an original geometric figure by moving all the points of the figure according to certain rules (the image of point A is called 'A', each point in the original corresponds to a point in the image)
Rigid transformation
A transformation in which the image is congruent to the original figure (rigid transformation is also called isometry)
Non-rigid transformation
A transformation in that does not preserve the size and shape of the figure
Three types of rigid transformations are
Translation, rotation, reflection
Translations (A slide)
A transformation in which each point of the image is the same distance from its corresponding point in the original figure (translation has distance and direction represented by a translation vector)
Rotation (A turn)
A transformation in which all points in the original are rotated an identical number of degrees about a fixed center point
Rotational symmetry
A figure that can be rotated about a point in such a way that its rotated image coincides with the original before turning a full 360� (circle)
Reflection
A transformation that produces a figure's mirror image
Line of Relection
The line where the mirror would be placed if viewing a reflected image (the line an image was reflected over)
Reflectional symmetry
If a figure can be reflected over a line in such a way that the resulting image coincides with the original, then the figure has a reflectional symmetry
Glide relection
A two-step transformation combining a translation with a reflection
Ordered pair rules
Used to transform polygons on a coordinate plane by relocating their verices
Compositions (of transformation)
When you apply one transformation to a figure and the apply another transformation to its image
Inductive reasoning
Process of observing data, recognizing patterns, and making generalizations about those patterns
Conjecture
A generalization (made in inductive reasoning)
Deductive reasoning
Process of showing that certain statements follow logically from agreed upon assumptions or proven facts
Paragraph proof
A logical argument written as a paragraph (uses deductive reasoning)
Converse
A converse of an "if..., then..." statement reverses the parts after the "if" and "then" (Are converses always true? No)
Transversal
A line intersecting two or more other lines in a plane
Corresponding angles
The angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
Alternate interior angles
When two lines are crossed by another line (which is called the Transversal), the pairs of angles on opposite sides of the transversal but inside the two lines are called Alternate Interior Angles.
Alternate exterior angles
When two parallel lines are cut by a transversal, the two pairs of angles on opposite sides of the transversal and outside the parallel lines, and the angles in each pair are congruent.
Same side interior angles
Another name for consecutive interior angles.
Sketch
A geometric diagram (not accurate) made using a pencil (freehand, no tools)
Construct
An accurate geometric diagram made using only a compass and straight edge
Draw
An accurate geometric diagram made using only a ruler and protractor
Segment bisector
A line, ray or segment that passes through the midpoint of a line segment
Perpendicular bisector
A line that divides the line segment into two congruent parts (bisects it) and is also perpendicular to it
Coincide
Lying exactly on top of each other (lines that coincide are identical and have all the same points)
Equidistant
The same from two points
Median
A line segment connecting a vertex of a triangle to the midpoint of the opposite side
Midsegment
A line segment connecting the midpoints of two sides of a triangle
Distance from a point to a line
The length of the perpendicular segment from the point to the line
Altitude
The perpendicular line segment connecting a vertex of a triangle to the opposite side of the triangle or the line containing the side
Angle bisector
A line, ray or line segment passing through the vertex of an angle that divided the angle into two congruent angles
Parallel lines
Lines in a given plane that never intersects
Slope
The rate of change between two variables
Y-intercept
The point where the graph crosses the y-axis
Auxiliary line
An additional line drawn in a diagram to help with a proof
Legs
The two congruent sides of an isosceles triangle
Isosceles triangle
A triangle with at least two congruent sides
Base angles
The angles between the base and each of the other two sides
Vertex angle
The angle between the two congruent sides
Exterior angle (of a triangle)
An angle created by extending one side of a triangle beyond it's vertext
Adjacent interior angle
An angle in a triangle which forms a linear pair with the exterior angle
Remote interior angles
Two angles of a triangle that do not share a vertex with the exterior angle
Included angle
The angle that is between two sides of a triangle
Included side
The side that is between two angles of a triangle
Flowchart
A concept map that shows all the steps of a complicated procedure in the proper order
Flowchart proof
A flowchart which comes to a conclusion as justified by logical reasons included in each step (box)
Biconditional statement
Included the phrase "if and only" only possible when the original statement and its converse are both true
N-gon
An "n" sided polygon
Exterior angle (of polygon)
An angle that forms a linear pair with one of the interior angles of a polygon
Kite
A quadrilateral with exactly two distinct pairs of congruent consecutive sides
Vertex angles (of kite)
The angles between the pairs of congruent sides
Non-vertex angles (of kite)
The angles between the pairs of non-congruent sides
Trapezoid
A quadrilateral with exactly one pair of parallel sides
Bases (of a trapezoid)
The parallel sides of a trapezoid
Base angles
A pair of angles that have a base as a common side (there are two sets of base angles in a trapezoid)
Isosceles trapezoid
A trapezoid whose two non-parallel sides are congruent
Midsegment (of a trapezoid)
The line segment connecting the midpoint of the two non-parallel sides
Vector
A directed line, usually represented by an arrow with a head and a tail, the direction of the vector is represented by the direction from tail to head. The vector length is the length of the line segment.
Resultant vector (or vector sum)
The result of combining two vectors
Rectangle
An equiangular parallelogram
Rhombus
An equilateral parallelogram
Square
An equiangular rhombus or an equilateral rectangle
Ratio
An expression that compares two quantities by division
Proportion
A statement of equality between two ratios
Similar figures
Figures that have the same shapes but not necessarily the same size
Similar polygons
Polygons with congruent corresponding angles and proportional corresponding sides
Scale factor
The ratio of corresponding lengths in similar figures
Dilation
A non-rigid transformation that enlarges or reduces a geometric figure by a scale factor relative to a point
Indirect measurement
Estimating a distance or a length by using properties of similarity or trigonometry