acute triangle
a triangle where all the angles are less than 90o
the leg of the right triangle next to the reference angle
altitude
a line segment of a triangle connecting a vertex to the line containing the opposite side and perpendicular to that side
altitude of a triangle
a line segment drawn or dropped perpendicular from the vertex of a triangle to the line containing the opposite side, the height of the triangle
angle Bisector
a ray that divides an angle into two equal parts
angle of depression
an angle measured below a particular reference point (usually a line of sight)
angle of elevation
an angle measured above a particular reference point (usually a line of sight)
apex
the vertex of a pyramid that is opposite from the base of a pyramid
apothem
the perpendicular length from the center of a regular polygon to its edge
arc
a curved line that is a part of a circle, a part of the circumference of a circle
arc length
the measure of the distance along the curved line of the circle, a segment of the circumference
area
the number of square units required to cover a give flat surface
axiom
a statement that is accepted as true
base
the congruent polygons that are parallel to each other on the top and bottom of a prism
bisect
to divide into two equal parts; the dividing line is called a bisector
central angle
an angle that intersects a circle in two points and whose vertex is the center of the circle chord
a line segment with two endpoints that lie on a circle
circumference
the perimeter of a circle; C = 2πr or C = dπ where C = circumference, r = radius, and d = diameter
composite figure
a figure made from two or more geometric figures
conjecture
an educated guess; a sentence that is either true or not true
conclusion
the “q” part of the conditional statement following the word “then,” the part to be proved
conditional statement
a statement written in the form if “p” then “q”
cone
a three-dimensional figure that has one circular base and one vertex
congruent
figures have the same shape and size, angles and sides have the same measures
congruent triangles
triangles with corresponding sides of the same length and corresponding interior angles of the same measure
conjecture
a statement believed to be true requiring proof
contrapositive statement
a statement exchanging and negating the hypothesis and conclusion of the original statement
converse statement
a statement exchanging the hypothesis and the conclusion of the original statement
corollary
a statement that follows directly from a theorem; a mini-theorem
corresponding parts
sides and angles that match up and are the same size shape and measure (congruent)
counterexample
an example which proves a conjecture is false
cross multiply
products of the means and extremes
cross-section
the plane figure which results when a 3-dimensional solid is intersected by a plane
cube
a rectangular prism with all sides congruent and all faces squares
cylinder
a three-dimensional geometric figure that has two congruent, parallel, circular bases
deductive reasoning
reasoning that arrives at a conclusion using facts, definitions, theorems, postulates, or properties
denominator
the bottom number in a fraction
diagonal
a segment in the interior of a polygon that connects non-adjacent vertices
diameter
a line segment that passes through the center of a circle with both its endpoints lying on the circle or sphere
dilation
a transformation that enlarges or reduces a figure
dimensions
used to describe the size and shape of an object
edge
the intersection of faces in a three-dimensional figure
enlargement
the result of dilation with a scale factor greater than 1
equiangular
all the angles of the polygon are congruent or have equal measures
equilateral
all the sides of the polygon are the same length or have equal measures
Euler's Formula
the number of vertices plus the number of faces less the number of edges equals 2
Euler's Theorem
the relationship between the number of faces, edges, and vertices in a polyhedron: VE + F = 2
exterior angle
extend each side of the regular polygon as shown below, no vertex will have more than one exterior angle
face
flat surface of a three-dimensional figure
geometric properties
attributes or characteristics of a geometric figure which are supported by definitions, postulates, or theorems
great circles
a circle on the surface of a sphere whose center is the center of the sphere
height
for a cylinder: the length of the segment perpendicular to both bases;
for a cone: the length of the segment perpendicular to the base and ending at the point of the cone
hypotenuse
the side opposite the right angle in a right triangle; it is the longest side of a right triangle hypothesis
the “p” part of the conditional statement following the word “if,” the given information
image
a figure from a transformation
included angle
an angle between two adjacent sides of a polygon; the segments representing the adjacent sides are included in the rays that create the angle
inductive reasoning
reasoning that arrives at a conclusion by generalizing a statement from observing patterns
inscribed angle
an angle which intersects a circle in two points and whose vertex is on the circle inscribed polygon
a polygon for which all of its vertices lie on a circle
inscribed square
a square whose vertices lie on a circle
intercepted arc
the arc of the circle which is in the interior of the inscribed angle interior angles
angles located inside the triangle, one at each vertex
inverse statement
a statement negating both the hypothesis and conclusion of the original statement
irregular polygon
a polygon whose sides are not all congruent to each other
isometric
representation of 3-Dimensional figures so that three sides of the figure can be observed
isosceles triangle
a triangle in which two sides are of equal length
justify
to provide a valid reason, possibly using postulates, theorems, corollaries, or definitions
lateral area
the sides:
lateral surface of a cylinder rectangle
lateral surface of a cone circular section
lateral edge
intersecting edges of the lateral faces of a solid
legs
the sides adjacent to the right angle in a right triangle line
holds location and has no thickness, length or width; it has no measure in any direction
line segment
a part of one line with two endpoints and all the points in between
linear pair
an interior angle paired wtih an exterior angle sharing the same side
median of a triangle
a line segment with endpoints that are a vertex of a triangle and the midpoint of the opposite side
minor arc
the shortest distance from one point on the circumference to another point on the circumference
multiple
the product of a number and any integer
negation
a statement formed by inserting the word “not” to change the meaning of the hypothesis or the conclusion to its opposite meaning
net
a two-dimensional picture of a three-dimensional figure that can be folded to form the figure
numerator
the top number in a fraction
oblique cone
a cone in which the height is not perpendicular to the base
oblique cylinder
a cylinder in which the bases are not aligned
oblique prism
a prism in which the bases are not aligned properly
obtuse triangle
a triangle with one angle larger than 90o but less than 180o (an obtuse angle
opposite leg
the leg of the right triangle opposite from the reference angle
orthographic
representation of 3-Dimensional figures using 2-Dimensional perspectives such as the Front, Side, or Top View
perfect square
the product of a squared integer or an integer to the second power
perpendicular
two lines or line segments intersecting to form 90o angles
plane
has length and width, but no thickness or height; a flat surface that extends infinitely in all directions along its length and width
point
holds location and has no thickness, length or width; it has no measure in any direction
point of tangency
the point where a tangent line intersects a circle
polygon
a closed plane figure formed by three or more line segments intersecting at their endpoints
polyhedron
a solid figure whose sides are polygons
postulate
a statement that is accepted as true without proof
pre-image
the original image before a transformation
prism
3-dimensional solid with 2 parallel and congruent bases named after the shape of the base
proportional
having a consistent ratio of all corresponding sides between two figures
pyramid
a three-dimensional figure with a polygon for a base and triangles for sides
Pythagorean Theorem
in a right triangle, where a and b are the lengths of the legs and c is the length of the hypotenuse, and a2 + b2 = c2
Pythagorean Triple
a set of three whole numbers that satisfy the Pythagorean Theorem
the distance from the center of the circle to any point on the circle's circumference or for a regular polygon, the length from the center to a vertex
ratio
a fraction
rate of change
the ratio of the change in the output value and change in the input value of a function
rectangular prism
a three dimensional object with six faces that are rectangles
reduction
the result of dilation with a scale factor less than 1
reference angle
one of the two acute angles of a right triangle that is the reference point
reflection
a transformation from a figure flipped across a line
regular polygon
an enclosed figure with all angles and all sides congruent
regular pyramid
a polyhedron with a polygonal base and triangles for sides, the height intersects the base at a right angle and the vertex
right angle
an angle that has a measure of 90o
right cone
a three-dimensional figure that has one circular base, one vertex and the height intersects the base at a right angle
right cylinder
a three-dimensional geometric figure that has two congruent and parallel bases and the height is perpendicular to both bases
right prism
a polyhedron consisting of two parallel, congruent faces called bases
right triangle
a triangle containing one interior angle with a measure of 90o (i.e. a right angle)
rotation
an image is rotated or turned around a point
scale factor
a positive number which describes the size change from a geometric figure to its image
scalene triangle
a triangle in which all three sides of the triangle are of different lengths
secant
a line that intersects a circle in two points
sector
a region of a circle at the center outlined by two radii and an arc or a piece of the circumference
segment
a line with two endpoints
segment of a circle
the portion of a circle bounded by the circle and the chord connecting the endpoints of two radii of the circle
semicircle
half a circle
semi-regular tessellation
a tessellation formed when two or more regular polygons with identical vertices
similar figures
figures which are the same shape but not necessarily the same size; corresponding sides are proportional and corresponding angles are congruent
slant height
the distance from the apex of a cone or pyramid to the base along the lateral surface of the solid
special right triangles
right triangles with angle measures of
30o-60o-90o
or
45o-45o-90o
sphere
a three dimensional figure where all the points are equidistant from a given point
straight angle
an angle with a measure of 180o
surface area
the sum of the areas of all its faces
supplementary angles
the sum of two angles equal 1800
symmetry
exact correspondence from one side of a dividing line or plan to the opposite sideof form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis
tangent
a line that intersects a circle in exactly one point
tessellate a plane
cover a plane with geometric figures with “no gaps-no overlaps”
tessellation
a repeated pattern covering a plane without any gaps or overlaps
theorem
a statement which has been shown to be true
tiling
polygons fit together to cover a play without gaps or overlaps
total surface area
the sum of the areas of all its faces
transformation
a change in the size or position of a figure
translation
the figure slides along a straight line
trapezoidal
three-dimensional shape which has at least one trapezoid as a face
truth value
a statement can have a value of true or false
vertex/vertices
a point at which the rays of an angle meet; the point at which two sides of a polygon meet; or where two or more edges of a polyhedron meet
volume
the number of cubic units required to fill a 3-dimensional space