Integrated Math 2 Ch. 10 Circle, Integrated Math 2 Geometry Review Vocabulary, Surface Area and Volume (VOCABULARY), Quadratics, Quadratic Vocabulary, Trigonometry, Geometry Vocabulary Final Review
Net
A 2-D digram of the surfaces and a 3-D figure that can be folded together to form the 3-D object.
Theta (θ)
A Greek letter that is often used to represent the measure of an angle.
Face
A flat surface.
Diameter
A line segment across the circle with each endpoint touching the circle and passing through the center. It is also a very specific chord.
Chord segment
A line segment whose TWO endpoints both intersect the circle.
Bisector
A line that divides something into two equal parts.
Common tagent
A line that is tangent to each of two coplanar circles. This tangent line can be tangent either internally or externally. A common internal tangent is a common tangent that intersects the segment that joins the center of the two circles
Pi
A mathematical constant and the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159
Arc
A part of the circle's circumference or a part of a curve.
Midpoint
A point that divides a segment into two congruent segments
Cube
A prism with six square faces. All other prisms and pyramids are named according to their base shape.
Trigonometric Ratio
A ratio of the lengths of two sides in a right triangle.
Circle
A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
Intercepted arc
A section of the circumference of a circle encased on either side by two different line segments that meet at one point, called a vertex.
External secant segment
A segment contained with an endpoint on the circle and at the fixed point outside the circle whose points all lie outside the circle except the endpoint on the circle.
Secant segment
A segment with one endpoint on a circle, one endpoint outside the circle, and one point between these points that intersects the circle.
conditional statement
A statement that can be written in if-then form
biconditional statement
A statement that can be written in the form "p if and only if q." This means "if p, then q" and "if q, then p" (p <--> q).
Tangent
A straight line (2D) or plane (3D0) that touches a curve or curved surface at ONE point, but if extended does not cross it at that point.
Right triangle
A triangle that has a 90 degree angle.
axis of symmetry
A vertical line that divides a parabola into 2 identical pieces
Domain
All of your x-values. For parabolas, it is all real numbers UNLESS it is a real world example. There's no such thing as negative seconds!!!
Range
All of your y-values.
Circumference
All points equal distance from the center, the enclosing boundary of a curved geometric figure, especially a circle.
Inscribed angle
An angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle.
Central angle
An angle whose apex (vertex) is the center of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. This angle is measured in radians.
Major arc
An arc of a circle having measure greater than 180 degrees
Radius
Any line segments from the circle's center to its perimeter (or circumference)
Y-intercept
Any point that intercepts the y-axis and when x is 0.
Zeros, Roots, and Solutions
Any point where y is 0, also know as x-intercepts.
Minor arc
Arc of a circle having measure less than 180 degrees
Congruent arcs
Arcs that are equal in size and shape. In the figure, two central angles of a circle are congruent as marked by the tic mark.
Concentric circles
Circles sharing the same center. An example is the archery target, featuring evenly spaced circles surrounding a "bulls eye". In geometry, two or more objects are said to be coaxal, or coaxial when they share the same center or axis.
Semi circle
Half of a circle
Angle Addition Postulate (AAP)
If an angle is split by a ray, then the sum of the measures of the smaller angles created is equal to the measure or the original angle.
Chord
In geometry, a line segment with TWO endpoints intersecting the circle's circumference. In music, a group of (typically three or more) notes sounded together, as a basis of harmony.
Adjacent arcs
Non-overlapping arcs with the same radius and center, sharing ONE common endpoint.
Point of tangency
Point at which a line touches an ellipse or circle, assuming that the line only makes contact at one point
trinomial
Polynomial with three terms
Congruent circles
Same size, same shape, and shares the same radius.
Volume
The amount of space an object takes up.
Surface Area
The area of all the faces of a 3D object added together. The area of a 3-D object's net.
Arc length
The distance along the arc (part of the circumference of a circle, or of any curve). For a circle, Arc Length = θ × r (when θ is in radians) or Arc Length = (θ × π/180 degrees) × r.
Center of a cirlce
The given point from which all points on a circle are the same distance
Vertex
The highest or lowest point of a parabola
Maximum
The highest point on your parabola
Distance
The length of a path between two points
Axis of Symmetry
The line that goes through the vertex. It is always written as x = #
Minimum
The lowest point on your parabola
Vertex
The point that is the intersection of three or more faces.
Cosine
The ratio of the adjacent side divided by the hypotenuse of a right triangle.
Tangent
The ratio of the side opposite divided by the adjacent side for a right triangle.
Sine
The ratio of the side opposite divided by the hypotenuse for a right triangle.
Edge
The segment that is intersection of two faces.
Hypotenuse
The side (leg) opposite the right angle in a right triangle.
Adjacent
The side (leg) that is next to your angle in a right triangle.
standard form of a quadratic
The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a ≠ 0.
Number of Solutions to a Quadratic
There can be 0, 1 or 2 solutions (x-intercepts)
Circumscribed
To draw a figure around another, touching the other figure at points but not cutting it. Typically, drawing a figure INSIDE a CIRCLE.
Supplementary angles
Two angles whose sum is 180°
Complementary angles
Two angles whose sum is 90 degrees.
Segment Addition Postulate (SAP)
Two smaller segments added together to equal to its whole.
deductive reasoning
Uses facts, rules, definitions or properties to arrive at a conclusion. Start with generalities and move to specifics.
inductive reasoning
Uses patterns to arrive at a conclusion (conjecture). Start with specifics and move to generalities
Opens Down
When the arrows point down and your a-value is negative.
Opens Up
When the arrows point up and your a-value is positive.
subtend
[verb] a line, arc, or figure form an angle at a particular point (B) when straight lines (line BA and line BC) from its extremities are joined at that point (B).
inscribed circle
a circle within a polygon, the circle being tangent to every side of the polygon
angle
a figure formed by two rays that have the same endpoint.
square
a four-sided figure with four right angles and four congruent sides
transversal
a line intersecting two or more lines in different points
vertical line
a line perpendicular to a horizontal line
altitude of a triangle
a line segment drawn from a vertex point perpendicular to the opposite side (base); the length is referred to as the height of the triangle.
chord
a line segment joining any two points on a circle
tangent to a circle
a line that intersects a circle at one- and only one- point on the circle
volume
a number describing the three-dimensional extent of a set
reciprocal
a number whose product with a given number is equal to 1
rhombus
a parallelogram with adjacent sides equal
line segment
a part of a line that consists of two points on the line, called endpoints, and all the points between them
polygon
a plan figure consisting of a certain number of sides
decagon
a polygon that has 10 sides
octagon
a polygon that has eight sides
pentagon
a polygon that has five sides
quadrilateral
a polygon that has four sides
hexagon
a polygon that has six sides
trapezoid
a polygon with four sides and exactly one pair of parallel sides
parallelogram
a polygon with four sides and two pairs of parallel sides
triangle
a polygon with three sides
sector
a portion of a circle bounded by two radii of the circle and one of the arcs they intercept
rectangle
a quadrilateral whose angles are right angles
cube
a rectangular prism whose six faces are squares
circle
a set of points in a plane at a given distance from a fixed point in a plane
cylinder
a space figure that has two circular bases that are the same size and are in parallel planes. It has one curved face.
cone
a space figure with one flat face (known as a base) that is a circle and with one other face that is curved
diameter
a straight line passing through the center of a circle and terminating at two points on the circle.
Secant
a straight line that passes through a circle at two different points or cuts a curve in two or more parts
segment of a circle
a the area between a chord and the arc being intercepted
isosceles trapezoid
a trapezoid whose non-parallel sides are equal
right triangle
a triangle that contains a right angle
acute triangle
a triangle whose three angles each measure less than 90 degrees
scalene
a triangle with no two sides equal
isosceles triangle
a triangle with two equal sides
equilateral
all sides are the same measure
obtuse
an angle greater than 90 degrees and smaller than 180 degrees
right angle
an angle measuring 90 degrees
exterior angle
an angle on a triangle formed by one side and the extension of the adjacent side
straight angle
an angle whose measure is 180 degrees
acute angle
an angle whose measure is less than 90 degrees
inscribed angle
an angle whose sides are chords of a circle and whose vertex is a point on the circle
major arc
an arc that is larger than a semi-circle
minor arc
an arc that is smaller than a semi-circle
Counterexample
an example that proves that a conjecture or statement is false
coordinates of a point
an ordered pair (x, y) specifying the distance of points from two perpendicular number lines (x- and y-axis)
point
an undefined element of geometry; it has position but no dimensions
inscribed polygon
any polygon which is inscribed in a shape
Pythagorean triples
any set of numbers that satisfies the Pythagorean theorem
parallel
equally distant; lines that never meet no matter how far they extend
vertex form of quadratic
f(x)=a(x-h)^2+k not equal to zero (h,k)
tangent of an angle
for an acute angle of a right triangle, the ratio of the length of the leg opposite the angle and the length of the leg adjacent to the angle
cosine of an angle
for an acute angle of a right triangle, the ratio of the length of the side adjacent to the angle and the hypotenuse
sine of an angle
for an acute angle of a right triangle, the ratio of the length of the side opposite the angle and the hypotenuse
congruent
having the same measure
central angle
in a circle, an angle whose vertex is the center and whose sides are radii
Pythagorean Theorem
in a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs A²+B²=C²
radius
line segment joining the center of the circle and a point on the circle
perpendicular
lines that meet and form right angles
quadrant
one of the four areas formed by the intersection of the x- and y-axis
semi-circle
one-half of a circle
circumscribed circle
or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.
Quadratic functions
polynomial equations that have a degree of 2; the highest exponent is 2
corresponding sides
sides of similar figures that are proportional
similar triangles
the angles are congruent and the sides are proportional
Trigonometry
the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.
circumference
the distance around a circle
proportion
the equality of two ratios
center of a circle
the fixed point in a plane about which a curve is equally distant.
parabola
the graph made by a quadratic function
maximum
the highest point on the graph; parabolas that open down have this
distance
the length of the line joining two points
diagonal
the line segment joining two non-adjacent vertices in a quadrilateral
proof
the logical argument that establishes the truth of a statement
vertex
the lowest or highest point on a parabola; also called the turning point
minimum
the lowest point on the graph; parabolas that open up have this
area
the measure of a surface; e.g. number of square units contained within a region
origin
the point of intersection of the x- and y-axis
y-intercept
the point where a graph crosses or touches the y-axis
sphere
the set of all points in space at a given distance from a fixed point
Opposite
the side (leg) that does not touch your angle in a right triangle.
hypotenuse
the side opposite the right angle in a right triangle; the longest side of a right triangle
legs
the sides of a right triangle adjacent to the right angle
perimeter
the sum of the lengths of the sides of a polygon
Pythagorean theorem
the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse
vertices of a triangle
the three points that form a triangle
base angles of a triangle
the two angles that have the base of the triangle as a common side
zeros, solutions, roots, x-intercepts
the value of x when y is 0
horizontal lines
these lines have a 0 slope; the equation is y= #
Collinear
three or more points that lie on the same line.
bisect
to divide in half
circumscribed
to draw a line around a figure
alternate interior angles
two angles formed by a line (the transversal) that cuts two parallel lines. The angles are interior angles on opposite sides of the transversal and do not have the same vertex
corresponding angles
two angles formed by a line (the transversal) that cuts two parallel lines. The angles, one exterior and one interior, are on the same side of the transversal.
adjacent angles
two angles having a common vertex and a common side between them
consecutive interior angles
two angles of a polygon with a common side
remote interior angles
two angles that are not adjacent to an exterior angle of a triangle
supplementary angles
two angles whose sum is 180 degrees
complementary angles
two angles whose sum is 90 degrees
vertical angles
two non-adjacent angles at a vertex formed when two lines intersect