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Math Exam Vocabulary and Important Terms/equations

Terms in this set (116)

Point
The most basic building block of geometry. It has no size or shape, only location (0-Dimensional)
Line
A continuous arrangement of infinitely many points. It has infinite length and extends forever in two directions (1-Dimensional)
Plane
A flat surface that extends infinitely along its length and width (2-Dimensional)
Collinear
On the same line
Coplanar
On the same plane
Line segment
Consists of 2 points (endpoints) and al the points between them are collinear
Congruent
MEASUREMENTS of figures are equal
Midpoint
The point on the segment that is the same distance from both endpoints (bisects the segment)
Ray
Has one endpoint and continues infinitely in one direction
Angle
Two rays that share a common endpoint (endpoint is the vertex)
Angle Bisector
Contains the vertex and divides the angle in half
Angle Addition Postulate
Two smaller interior angles will equal the larger angle
Steps to creating a good definition
1. Classify your term (what is it)
2. Differentiate your term (how does it differ from others)
3. Test by looking for a counterpart
Parallel
Never intersects, lines have the same slope
Perpendicular
Intersect to form 4 right angles
Complementary Angles
Angles who's measures add up to 90 degrees (don't have to be adjacent)
Supplementary Angles
Angles who's measures add up to 180 degrees (don't have to be adjacent)
Vertical Angles
Opposite Angles formed by 2 intersecting lines (congruent measures)
Linear Pair of angles
ADJACENT angles that form a line who's measure is 180 degrees
Skew Lines
Lines that never intersect because they're on different planes
Polygon
A closed figure in a place, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly 2 others
3 sided figure
triangle
4 sided figure
quadrilateral
5 sided figure
Pentagon
6 sided figure
Hexagon
7 sided figure
Heptagon
8 sided figure
Octagon
9 sided figure
Nonagon
10 sided figure
Decagon
11 sided figure
Undecagon
n sided figure
n-gon
Consecutive Angles
Angles that are next to each other
Naming Polygons
List the vertices in consecutive order
Diagonal
A line segment that connects 2 non-consecutive vertices
Convex
no diagonals fall outside of the polygon
Concave
one or more diagonals are outside the polygon
Congruent Polygon
Corresponding sides and angles are congruent, same size and shape
Perimeter
The sum of the measurements of the sides
Equilateral Polygon
A polygon in which all sides are congruent
Equiangular Polygon
A polygon with all congruent angles
Regular Polygon
A polygon with congruent angles and sides
Right Triangle
Triangle with one right angle
Acute Triangle
A triangle with all angles less than 90 degrees
Obtuse Triangle
A triangle with one angle greater than 90 degrees
Scalene Triangle
All sides different length
Equilateral Triangle
All sides and angles are the same
Isosceles Triangle
At least 2 sides are congruent
Trapezoid
A quadrilateral with one set of parallel sides
Kite
A quadrilateral with 2 pairs of consecutive, congruent sides
Parallelogram
A quadrilateral with 2 sets of parallel sides
Rhombus
A parallelogram with all sides congruent
Rectangle
Parallelogram with 4 right angles
Square
Rectangle with 4 congruent sides
Circle
set of all points in a plane at a given distance from a given point
Radius
The distance from the center of a circle to the outside (half the diameter)
Center
A given point that names the circle (in the very center roof the circle)
Chord
Segments whose endpoints lie on the circle
Diameter
A chord that passes through the center of a circle (longest possible chord in a circle)
Tangent
A line that touches the circle at only one point (perpendicular to the radius)
Circumscribed
Circle (or other polygon) is circumscribed about a polygon if it passes through each vertex of the polygon
Inscribed
A polygon is inscribed in a circle if each one of its vertexes is passed through by a circle (or other polygon)
Concentric
They are inside of another but share the same midpoint (the circle and square are concentric)
Arc
Part of a circle that is 2 point on a circle
Minor Arc
Arc is smaller than a semi-circle (define it with 2 points)
Major Arc
Larger than a semi-circle (define it with 3 points)
Arc Measure
The measure of the angle that the arc makes (major arc=360-minor arc)
Space
Three dimensional, set of all points
Isemetric Drawing
Drawing 3-dimensions on a 2-dimensional surface
Cylinder
Circles as the bases
Cone
Circle as base, the top is a point
Pyramid
Can have any regular polygon as a base, ends in a point
Prism
Can have any regular polygon as its to bases
Hemisphere
Sphere cut in half
Sphere
Globe-shape
Transformation
Moving a figure in space
Types of transformation
Translation, Reflection, Rotation
Translation
Moving every vertices of a figure on a parallel path
Translation Vector
The direction in which the vertices are moved in a translation
Rotation
Figure is rotated around a center point
Reflection
Mirror image of a figure (line of reflection divides it)
Ven-diagram
Represents characteristics that sets have in common
Visual Reasoning
Looking at drawings to infer something
Inductive Reasoning
The process of observing data, recognizing PATTERNS, and making generalizations about the patterns
Deductive Reasoning
The process of showing that certain statements follow logically from agreed-upon assumptions and proven FACTS (explains why something works)
Deductive vs. Inductive
Deductive proves conjecture, inductive finds conjecture
Conjecture
An assumption made my using inductive reasoning
Converse
The opposite of an "if-then statement"
Transversal
A line intersecting parallel lines
Corresponding angles
Same location, but on different parallel lines (congruent)
Alternate Interior Angles
Either side of the transversal, but on the inside
Consecutive Interior Angles
Supplementary angles
Consecutive Exterior
Supplementary angles
3 congruency postulates
SSS (side side side), SAS (side angle side), ASA (angle side angle)
SSS
All 3 sides are congruent (have to be corresponding)
SAS
2 corresponding sides and an included angle are congruent
ASA
2 corresponding angles and an included side are congruent
Right Triangle congruency Postulates
HL (hypotenuse Leg), HA (Hypotenuse Angle)
HL
The hypotenuse and a corresponding side is congruent
HA
The hypotenuse and a corresponding angle is congruent
Altitude
A PERPENDICULAR segment drawn from a vertex to the opposite side
Median
A segment drawn from a vertex the midpoint of the opposite side
CPCTC
corresponding parts of congruent triangles are congruent
Reflexive Property
When sides or angles are congruent to themselves
Sum of the interior angles
180(n-2)
Measure of one angle in a regular polygon
180(n-2)/n
Sum of the exterior angles
360 degrees (always)
Measure of the exterior angle measure of 1 angle of a regular polygon
360/n
When two planes intersect, what do they form
A line
When two lines intersect, what do they form
A point
Properties of parallelograms
2 pairs of parallel sides, opposite sides congruent, opposite angles congruent, consecutive angles supplementary, diagonals bisect each other
Properties of kites
two pairs of consecutive sides are congruent, diagonals are perpendicular, non-vertex angles are congruent, diagonal bisects vertex angles
Properties of Isosceles Trapezoids
Non-parallel sides congruent, diagonals are congruent, base angles are congruent, consecutive non base angles are supplementary
Properties of Rectangles
Opposite sides congruent, opposite sides parallel, opposite angles congruent, consecutive angles supplementary, diagonals are congruent, diagonals bisect each other, all vertex angles measure 90 degrees
Properties of Rhombuses
Opposite sides are parallel, opposite angles are congruent, consecutive angles supplementary, diagonals bisect each other, all sides are congruent, diagonals bisect vertex angles
Properties of Squares
Opposite sides are parallel, opposite angles are congruent, consecutive angles are supplementary, diagonals bisect each other, diagonals are congruent, all vertex angles measure 90 degrees, diagonals are perpendicular, all sides are congruent, diagonals bisect vertex angles,.
Dilation
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
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