208 terms

Geometry Vocabulary (Cumulative)

Vocab, figures, etc. From chapter 1 until now!
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Point
Location with no size, named with a capital letter.
Line
Straight path with no thickness & extends forever, named with 2 points and a symbol above or a cursive letter.
Plane
Flat surface with no thickness and extends forever, named with 3 non-collinear points or a cursive capital letter.
Collinear
Points on the same line.
Non-Collinear
Points NOT on the same line.
Segment
Part of a line consisting of 2 points and everything in between, named with the 2 endpoints and a symbol above.
Ray
Part of a line that starts at an endpoint and extends forever in one direction, named with the endpoint and another point with a symbol above.
Opposite Rays
Two rays that have a common endpoint and form a line.
Postulate
Statement that is accepted as true without proof.
Distance/length
Absolute value of the difference of the coordinates of two points.
Congruent Segments
Segments that have the same length, marked with tick marks.
Construction
Way of creating a figure that is more precise, using a compass, straightedge, etc.
Midpoint
The point that divides a segment into two congruent segments.
Bisect
To divide something in half.
Segment Bisector
Any ray, segment, or line that intersects a segment at its midpoint.
Angle
Figure formed by 2 rays with a common endpoint.
Degree
1/360 of a circle.
Acute Angle
Angle less than 90, but greater than 0.
Right Angle
90 degree angle.
Obtuse Angle
Angle greater than 90, but less than 180.
Straight Angle
180 degree angle.
Congruent Angles
Angles with the same degree measure.
Angle bisector
A ray that divides an angle into two congruent angles.
Adjacent Angles
Angles that share a common endpoint and a common side.
Linear Pair
Pair of adjacent angles that form a line.
Complementary Angles
2 angles whose measures add to 90 degrees.
Supplementary Angles
2 angles whose measures add to 180 degrees.
Vertical Angles
2 angles across from each other in an "X" (non-adjacent)
Perimeter
Sum of the side lengths of a figure (or distance around a figure).
Area
number of non-overlapping square units of a given size that exactly cover a figure.
Diameter
Segment that passes through the center of a circle and whose endpoints are on the circle.
Radius
Segment whose endpoints are the center of the circle and a point on the circle.
Pi
The ratio of a circle's circumference to its diameter.
Hypotenuse
The side of a triangle across from the right angle (the longest side).
Midpoint Formula
( (X1+X2)/2 , (Y1+Y2)/2 )
Distance Formula
Sqrt( (X2-X1)^2 + (Y2-Y1)^2 )
Transformation
Change in position, size, or shape of a figure.
Pre-image
The original figure.
Image
The new figure.
Reflection
Transformation across a line.
Rotation
Transformation about a point.
Translation
Transformation in which all points move the same distance in the same direction.
Mrs. Lewis
The coolest teacher ever!
Inductive Reasoning
The process of reasoning that a rule or statment is true because specific cases are true.
Conjecture
A statement you believe to be true based on inductive reasoning.
Counterexample
An example that shows a conjecture is not true.
Conditional Statement
If p, then q.
Converse
If q, then p.
Inverse
If not p, then not q.
Contrapositive
If not q, then not p.
Negation
NOT p.
Logically equivalent statements
Statements that have the same truth value. (Conditional & Contrapositive) (Converse & Inverse)
Deductive Reasoning
The process of using logic to draw conclusions from given facts, definitions, and properties.
Law of Detachment
If p->q is true and p is true, then q is true.
Law of Syllogism
If p->q and q->r are true, then p->r is true.
Biconditional
p if and only if q.
Polygon
Closed plane figure formed by three or more line segments.
Triangle
3 sided polygon.
Quadrilateral
4 sided polygon.
Proof
An argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.
Theorem
Any statement you can prove.
2 Column Proof
Proof in which steps of the proof are listed on the left, with justification given on the right.
Flowchart Proof
Proof which uses boxes and arrows to show the structure of the proof.
Paragraph Proof
Proof that presents the steps & reasons of a proof as sentences in a paragraph.
Parallel Lines
Coplanar lines that do not intersect.
Perpendicular Lines
Lines that intersect at 90 degree angles.
Skew Lines
Lines that are noncoplanar, are not parallel, and do not intersect.
Parallel Planes
Planes that do not intersect.
Transversal
A line that intersects two coplanar lines at two different points.
Corresponding Angles
Angles that lie on the same side of the transversal and on the same sides of the two crossing lines.
Alternate Interior Angles
Angles that lie on opposite sides of the transversal, between the two crossing lines.
Alternate Exterior Angles
Angles that lie on opposite sides of the transversal, outside the two crossing lines.
Same-Side Interior Angles
Angles on the same side of the transversal between the two crossing lines.
Perpendicular Bisector
A line perpendicular to a segment at the segment's midpoint.
Distance from a point to a line
The length of the perpendicular segment from the point to the line.
Slope
Rise/Run. (Y2 - Y1) / (X2 - X1).
Point-Slope Form
Y - Y1 = m(X - X1)
Slope-Intercept Form
y = mx+b
Equation of a Horizontal Line
y = a
Equation of a Vertical Line
x = a
Parallel Lines
Same slope, different y-intercept.
Intersecting Lines
Different slopes
Coinciding Lines
Same slope, same y-intercept.
Acute Triangle
triangle with 3 acute angles
Equiangular Triangle
triangle with 3 congruent angles
Right Triangle
triangle with 1 right angle
Obtuse Triangle
triangle with 1 obtuse angle
Equilateral Triangle
triangle with 3 congruent sides
Isosceles Triangle
triangle with at least 2 congruent sides
Scalene Triangle
triangle with no congruent sides
Auxiliary Line
line added to a figure to aid in a proof
Corollary
theorem whose proof follows directly from another theorem
Interior
set of all points inside a figure
Exterior
set of all points outside a figure
Interior Angle
an angle formed by two sides of a triangle
Exterior Angle
an angle formed by one side of a triangle and the extension of an adjacent side
Remote Interior Angle
an interior angle that is not adjacent to the exterior angle
Congruent Polygons
polygons with congruent corresponding angles and sides (same size and same shape)
Included Angle
an angle formed by 2 adjacent sides of a polygon
Included Side
common side of 2 consecutive angles in a polygon
CPCTC: Corresponding Parts of Congruent Triangles are Congruent
can be used as a justification in a proof after you have proven the triangles congruent
Coordinate Proof
style of proof that uses coordinate geometry and algebra
Vertex Angle
an angle formed by the 2 legs of an isosceles triangle
Base Angles
angles formed by a leg and the base of an isosceles triangle
Equidistant
when a point is the same distance from 2 or more objects
Locus
set of points that satisfies a given condition
Concurrent
when 3 or more lines intersect at one point
Point of Concurrency
the point where 3 or more lines meet
Circumcenter of a Triangle
the point of concurrency of the 3 perpendicular bisectors of a triangle
Circumscribed Circle
a circle that contains all the vertices of a polygon
Incenter of a Triangle
the point of concurrency of the 3 angle bisectors of a triangle
Inscribed Circle
a circle in a polygon that intersects each side of the polygon once
Median of a Triangle
a segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side
Centroid of a Triangle
the point of concurrency of the 3 medians of a triangle
Altitude of a Triangle
a perpendicular segment from a vertex to the line containing the opposite side in a triangle
Orthocenter of a Triangle
the point of concurrency of the 3 altitudes of a triangle
Midsegment of a Triangle
a segment that joins the midpoints of 2 sides of a triangle
Indirect Proof
type of proof which begins by assuming the conclusion is false and seeks to reach a contradiction
Pythagorean Triple
a set of 3 nonzero whole numbers a, b, and c, such that a^2+b^2=c^2
Diagonal
a segment that connects any two nonconsecutive vertices of a polygon
Regular Polygon
polygon that is both equilateral and equiangular
Concave
a polygon with any part of a diagonal containing points in the exterior of the polygon
Convex
a polygon where no diagonals are in the exterior
Parallelogram
a quadrilateral with two pairs of parallel sides
Rectangle
a quadrilateral with four right angles
Rhombus
a quadrilateral with four congruent sides
Square
a quadrilateral with four right angles and four congruent sides
Kite
a quadrilateral with exactly two pairs of congruent consecutive sides
Trapezoid
a quadrilateral with exactly one pair of parallel sides
Isosceles Trapezoid
a trapezoid in which the two legs are congruent
Midsegment of a Trapezoid
segment whose endpoints are midpoints of the legs of a trapezoid
Ratio
comparison of two numbers by division
Proportion
equation stating that two ratios are equal
Cross Products
the product of the extremes ad and the product of the means bc
Similar
figures that have the same shape but not necessarily the same size
Similar Polygons
polygons with congruent corresponding angles and proportional corresponding side lengths
Similarity Ratio
ratio of the lengths of the corresponding sides of two similar polygons
Indirect Measurement
any method that uses formulas, similar figures, and/or proportions to measure an object
Scale Drawing
represents an object as smaller or larger than its actual size
Scale
the ratio of any length in a drawing to the corresponding actual length
Dilation
transformation that changes the size of a figure but not its shape
Scale Factor
describes how much a figure is enlarged or reduced
Geometric Mean
the square root of a product of two numbers
Trigonometric Ratio
ratio of two sides of a triangle
Sin
opposite/hypotenuse
Cos
adjacent/hypotenuse
Tan
opposite/adjacent
Inverse Trig Functions
used to find angles of a right triangle
Angle of Elevation
angle measured upward from a horizontal
Angle of Depression
angle measure downward from a horizontal
Law of Sines & Law of Cosines
used to find angles or sides of non-right triangles
Vector
quantity with both magnitude and direction
Component Form
lists the horizontal and vertical change of a vector
Magnitude
length of a vector
Direction
angle a vector makes with a horizontal line
Equal Vectors
have the same magnitude and direction
Parallel Vectors
have the same or opposite directions
Resultant Vector
sum of two vectors
Area of a Parallelogram
A=bh
Area of a Triangle
A=1/2bh
Area of a Trapezoid
A=1/2(b1+b2)h
Area of a Rhombus/Kite
A=1/2d1*d2
Area of a Circle
A=pi*r^2
Circumference of a Circle
A=2pir
Area of a Regular Polygon
A=1/2aP
Composite Figure
is made up of simple shapes, such as triangles, rectangles, and trapezoids
Geometric Probability
The probability of an event based on a ratio of geometric measures such as length or area
Face
flat surface of a 3D figure
Edge
where two faces intersect on a 3D figure
Vertex
where three or more faces intersect on a 3D figure
Prism
formed by two parallel congruent polygonal faces connected by parallelograms
Cylinder
formed by two parallel congruent circle bases connected by a curved surface
Pyramid
formed by a polygonal base and triangular faces that meet at a vertex
Cone
formed by a circular base and a curved surface that connects the base to the vertex
Net
diagram of the surfaces of a 3D figure that can be folded to form it
Orthographic Drawing
shows 6 different views of an object: front, back, right, left, top, bottom
Isometric Drawing
way to show three sides of a figure from a corner view
Perspective Drawing
way to show depth to a figure by drawing things that are farther away smaller
Polyhedron
formed by four or more polygons that intersect only at the edges
Space
set of all points in 3D
Euler's Formula
V-E+F=2
Surface Area
the total area of all faces and curved surfaces of a 3D figure
Lateral Area
sum of the areas of the lateral faces of a 3D figure
Volume
the number of nonoverlapping unit cubes that will exactly fill the interior of a 3D figure
Sphere
locus of points in spaces that are a fixed distance from a given point called the center
Hemisphere
half a sphere
Great Circle
divides a sphere into two hemispheres
Interior of a Circle
the set of all points inside a circle
Exterior of a Circle
the set of all points outside a circle
Chord
segment whose endpoints lie on a circle
Secant
line that intersects a circle at 2 points
Tangent
line that intersects a circle at one point
Congruent Circles
circles with the same radii
Concentric Circles
coplanar circles with the same center
Tangent Circles
coplanar circles that intersect at one point
Central Angle
an angle whose vertex is the center of a circle
Arc
an unbroken part of a circle consisting of two points and all points between them
Semicircle
half of a circle
Adjacent Arcs
arcs of the same circle that intersect at exactly one point
Congruent Arcs
arcs with the same measure
Sector of a Circle
region bounded by two radii of a circle and their intercepted arc
Segment of a Circle
region bounded by an arc and its chord
Arc Length
distance along an arc, measured in linear units
Inscribed Angle
an angle whose vertex is on a circle and whose sides contain chords of the circle
Intercepted Arc
consists of endpoints that lie on the sides of an inscribed angle and all points between them
Secant Segment
segment of a secant with at least one endpoint on the circle
External Secant Segment
secant segment that lies in the exterior of the circle with one endpoint on the circle
Tangent Segment
segment of a tangent with one endpoint on the circle
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