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Things that are on the geometry regents
Terms in this set (214)
acute angle
an angle whose measure is between 0° and 90°
acute triangle
a triangle with three acute angles
adjacent angles
two coplanar angles that have a common side and a common vertex but no common interior points
adjacent arcs
arcs that are on the same circle and have exactly one point in common
alternate interior/exterior angles
nonadjacent interior/exterior angles that lie on opposite sides of the transversal
altitude of a triangle
a perpendicular segment in a triangle from a vertex to the line containing the side opposite that vertex
angle
formed by two rays with the same endpoint
angle bisector
a ray that divides an angle into two congruent angles
angle of elevation or depression
the angle formed by a horizontal line and the line of sight to an object above/below the horizontal line
apothem
the distance from the center of a regular polygon to the side
arc length
the product of the ratio (measure of the arc / 360) and the circumference of the circle
area
the number of square units enclosed by a plane figure
biconditional
the combination of the conditional statement and its converse; contains the words "if and only if"
iff
if and only if
central angle of a circle
an angle whose vertex is the center of the circle
central angle of a regular polygon
an angle formed by two consecutive radii
centroid
the point of concurrency of the medians of a triangle
chord
a line segment whose endpoints are on a circle
circumcenter
the point of concurrency of the perpendicular bisectors of the sides of a triangle
circumference
the distance around a circle (C = 2πr)
circle circumscribed about polygon
when all vertices of polygon are on circle
polygon circumscribed about circle
when all the sides of a polygon are tangent to the circle
collinear points
when points lie on the same line
compass
a geometric tool used to draw arcs and circles
complementary angles
when the sum of the measures of two angles is 90°
composite space figures
the combination of two or more figures into one object
concentric circles
circles that lie in the same plane and have the same center
conclusion
part of the "if-then" statement (conditional) that follows "then"
concurrent lines
three or more lines that meet at the same point
point of concurrency
point at which concurrent lines meet
conditional
an "if-then" statement
cone
a three-dimensional figure that has a circular base, a vertex not in the plane of the circle, and a curved lateral surface
altitude of a cone
the perpendicular segment from the vertex to the plane of the base
height of a cone
the length of the altitude of the cone
right cone
cone in which the center contains the altitude of the base
slant height of a cone
the distance from the vertex to the edge of the base
congruent angles
angles that have the same measure
congruent arcs
arcs that have the same measure and are in the same or congruent circles
congruent circles
circles whose radii are congruent
congruent polygons
polygons that have corresponding sides congruent and corresponding angles congruent
congruent segments
segments that have the same length
conjecture
a conclusion reached by using inductive reasoning
consecutive angles
angles of a polygon which share a common side
construction
a geometric figure made with only a straightedge and a compass
contrapositive (of the conditional "if p, then q")
if not p, then not q
converse (of the conditional "if p, then q")
if q, then p
coordinates(s) of a point
the distance and direction from the origin of a number line (x,y)
coordinate plane
formed by two axes, intersecting at two angles
axes
number lines
axis
number line
x-axis
the horizontal axis
y-axis
the vertical axis
quadrants
what the axes divide the coordinate plane into; four of them
coplanar figures
figures in the same plane
corollary
a statement that follows directly from a theorem
corresponding angles
congruent angles that lie on the same side of a transversal intersecting two lines and in corresponding positions relative to the two lines
counterexample
a particular example or instance that makes a statement false
CPCTC
corresponding parts of congruent triangles are congruent
cross-product property
the product of the extremes of a proportion is equal to the product of the means
cross-section
the intersection of a solid and a plane
cube
a polyhedron with six faces, each of which is a square
cylinder
a three-dimensional figure with two congruent circular bases which lie in parallel planes
altitude of a cylinder
a perpendicular segment that joins the planes of the bases
height of a cylinder
the length of the altitude of the cylinder
right cylinder
the segment joining the centers of the bases of the cylinder is an altitude
oblique cylinder
the segment joining the centers of the bases is not perpendicular to the planes containing the bases
decagon
a polygon with ten sides
deductive reasoning
a process of reasoning logically from given facts to reach a conclusion
diameter of a circle
a chord that contains the center of a circle
diameter of a sphere
a line segment passing through the center of the sphere, with endpoints on the sphere
dilation
a transformation which enlarges or reduces a figure; the center of a dilation is its own image
distance from a point to a line
the length of the perpendicular segment from the point to the line
dodecagon
a polygon with twelve sides
equiangular polygon
a polygon whose angles are all congruent
equilateral polygon
a polygon whose sides are all congruent
equivalent statements
statements with the same truth value
Euclidean geometry
a geometry of the plane in which Euclid's parallel postulate is true
exterior angle of a polygon
an angle of a polygon formed by a side and an extension of an adjacent side
foundation drawing
shows the base of a structure and the height for each part
geometric mean
the number x such that (a/x) = (x/b), where a, b, and x are all positive numbers
geometric probability
a probability that uses a geometric model in which points represent outcomes
glide reflection
the composition of a translation followed by a reflection across a line parallel to the translation vector
glide reflectional symmetry
the type of symmetry for which there is a glide reflection that maps a figure onto itself
golden rectangle
a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle
golden ratio
the ratio of the length of a golden rectangle to its width, (1+ √5)/2, or about 1.62
great circle
the intersection of a sphere and the plane containing the center of the sphere; divides the sphere into two hemispheres
hexagon
a polygon with six sides
hypothesis
the part that follows "if" in an "if-then" statement (conditional)
identity
an equation that is true for all allowed values of the variable
incenter of a triangle
the point of concurrency of the angle bisectors of the triangle
indirect measurement
a way of measuring things that are difficult to measure directly
indirect reasoning
a type of reasoning in which all possibilities are considered and then the unwanted ones are proved false, so that the remaining ones must be true
inductive reasoning
a type of reasoning that reaches conclusions based on a pattern of specific examples or past events
circle inscribed in a polygon
when all the sides of the polygon are tangent to the circle
polygon inscribed in a circle
when the vertices of the polygon are on the circle
inscribed angle
when the vertex of an angle is formed by two chords; the measure of the angle is half of the measure of the intercepted arc formed by the two chords
intercepted arc
an arc of a circle having endpoints on the sides of an inscribed angle, and its other points in the interior of the angle
inverse (of the conditional "if p, then q")
if not p, then not q
isometry
a transformation in which an original figure and its image are congruent
isosceles trapezoid
a trapezoid whose nonparallel sides are congruent
isosceles triangle
a triangle that has at least two congruent sides
kite
a quadrilateral with two pairs of congruent adjacent sides and no opposite sides congruent
lateral area (of a prism/pyramid)
the sum of the areas of the lateral faces
lateral area (of a cylinder/cone)
the area of the curved surface
line (Euclidean geometry)
a series of points that extend in two directions without end (technically undefined)
locus
a set of points, all of which meet a stated condition
major arc
an arc that is larger than a semicircle
measure of an angle
a number of degrees greater than 0 and less than or equal to 180; can be measured with a protractor
measure of an arc
the measure of the arc's central angle; measure of major arc can be found by subtracting the measure of the minor arc from 360, and vice versa
median of a triangle
a segment that has as its endpoints a vertex of a triangle and the midpoint of its opposite side
midpoint of a segment
the point that divides the segment into two congruent segments
midsegment of a trapezoid
the segment that joins the midpoints of the nonparallel opposite sides of a trapezoid
midsegment of a triangle
the segment that joins the midpoints of two of the sides of the triangle
minor arc
an arc smaller than a semicircle
negation (of a statement)
has the opposite meaning of the original statement
n-gon
a polygon with n-sides
net
a two-dimensional figure that you can fold to form a three-dimensional figure
nonagon
a polygon with nine sides
obtuse angle
an angle whose measure is between 90° and 180°
octagon
a polygon with eight sides
opposite rays
collinear rays with the same endpoint; form a line
orthocenter
the point of intersection of the lines containing the altitudes of the triangle
parallel lines
two or more coplanar lines that do not intersect
parallelogram
a quadrilateral with two pairs of parallel sides; any side can be called a base
pentagon
polygon with five sides
perimeter of a polygon
the sum of the lengths of the polygon's sides
perpendicular bisector
a line, segment, or ray that is perpendicular to a segment at its midpoint
perpendicular lines
lines that intersect to form right angles
pi (π)
the ratio of the circumference of any circle to its diameter; irrational number
plane
a flat surface with no thickness; contain infinite lines that extend in all directions (Euclidean geometry technically undefined)
point
a location; no size (Euclidean geometry technically undefined)
point symmetry
the type of symmetry for which there is a rotation of 180° that maps the figure onto itself
point-slope form
y-y1 = m(x-x1)
polygon
a closed plane figure with at least three sides that are segments; sides intersect only at their endpoints; no two adjacent sides are collinear
diagonal
a segment that connects two nonconsecutive points in a polygon
vertex/verticies
endpoints of sides in a polygon or polyhedron
convex polygon
when no diagonal contains points outside the polygon
concave polygon
when a diagonal contains points outside the polygon
polyhedron
a three-dimensional figure whose faces are polygons
edges
where faces of a polyhedron intersect
postulate
an accepted statement of fact
prism
a polyhedron with two congruent and parallel faces, which are called the bases; the other faces which are parallelograms are called lateral faces
proof
a convincing argument that uses deductive reasoning
two-column proof
statements and reasons are aligned in columns
paragraph proof
statements and reasons are connected in sentences
flow proof
shows the logical connections between the statements
coordinate proof
a figure is drawn on a coordinate plane and the formulas for slope, midpoint, and distance are used to prove properties of the figure
indirect proof
involves the use of indirect reasoning
proportion
a statement that two ratios are equal
extended proportion
a statement that three or more ratios are equal
pyramid
a polyhedron in which one face (the base) is a polygon, and the other faces (lateral faces) are triangles with a common vertex
regular pyramid
a pyramid whose base is a regular polygon and whose sides are isosceles triangles
slant height (pyramid)
the length of the altitude of a lateral face
Pythagorean theorem
a^2 + b^2 = c^2, when a and b are the legs of a right triangle, and c is the hypotenuse
hypotenuse
the side of a right triangle opposite the right angle
Pythagorean triple
a set of three nonzero whole numbers (a, b, and c) that satisfy the equation, a^2 + b^2 = c^2
quadrilateral
a polygon with four sides
radius of a circle
any line segment with one endpoint on the circle and the other endpoint at the center of the circle
radius of a regular polygon
the distance to the center of the regular polygon to a vertex
radius of a sphere
any line segment that has one endpoint at the center of the sphere and the other endpoint on the sphere
ratio
a comparison of two quantities by division
ray
the part of the line consisting of one endpoint and all the other points of the line on one side of the endpoint
rectangle
a parallelogram with four right angles
refection
a transformation in which the image of the figure is the mirror image of the preimage
reflectional symmetry (line symmetry)
a type of symmetry for which there is a reflection that maps a figure onto itself
regular polygon
a polygon that is both equiangular and equilateral
resultant vector
the sum of two vectors
rhombus
a parallelogram with four congruent sides
right angle
an angle whose measure is 90°
right triangle
a triangle that contains one right angle
rotation
a transformation that turns a figure about a fixed point
rotational symmetry
the type of symmetry for which there is a rotation of 180° or less that maps a figure onto itself
scale
the ratio of any length in a scale drawing to the corresponding actual length; the lengths may be in different units
scale drawing
a drawing in which all lengths are proportional to corresponding actual lengths
scale factor
the number that describes the size change from an original figure to its image
scalene triangle
a triangle that has no congruent sides
secant
a line, ray, or segment that intersects a circle at two points
sector of a circle
the region bounded by two radii and their intercepted arc
line segment
the part of a line consisting of two endpoints and all points between them
segment bisector
a line, segment, ray, or plane that intersects a segment at its midpoint
segment of a circle
the part of a circle bounded by an arc and the segment joining its endpoints
semicircle
half of a circle
similar polygons
polygons having corresponding angles congruent and corresponding sides congruent
similar solids
solids that have the same shape and all of their corresponding dimensions are proportional
similarity ratio
the ratio of the lengths of corresponding sides of similar figures
skew lines
noncoplanar lines
slope-intercept form (linear equation)
y = mx + b, where m is the slope of the line and b is the y-intercept
slope of a line
the ratio of a line's vertical change in a coordinate plane to its horizontal change; Δy/Δx
space
the set of all points
sphere
the set of all points in a space that are a given distance (radius) from a given point (center)
square
a parallelogram with four congruent sides and four right angles
standard form of an equation of a circle
(x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle
straight angle
an angle whose measure is 180°
supplementary angles
angles whose measures add up to 180°
surface area (of a prism, cylinder, pyramid, or cone)
the sum of the lateral area and the areas of the bases
surface area (of a sphere)
four times the area of the great circle
symmetry
when there is an isometry that maps the figure onto itself
tangent to a circle
a line, line segment, or ray in the plane of the circle that intersects the circle in exactly one point
theorem
a conjecture that is proven
transformation
a change in the position, size, or shape of the geometric figure
translation
a transformation that moves points the same distance and in the same direction
transversal
a line that intersects two coplanar lines in two points
trapezoid
a quadrilateral with exactly one pair of parallel sides (the bases)
triangle
a polygon with three sides
trigonometric ratios
sine, cosine, and tangent
tangent ratio
tanΘ=opposite/adjacent
cosine ratio
cosΘ=adjacent/hypotenuse
sine ratio
sinΘ=opposite/hypotenuse
truth value (of a statement)
either "true" or "false", depending on whether the statement is true or false, respectively
vector
any quantity that has magnitude and direction
initial point
starting point of the arrow that represents a vector
terminal point
the ending point that an arrow that represents a vector points to
vertical angles
two angles whose sides form two pairs of opposite rays
volume
a measure of the space a figure occupies
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