Geometry Vocabulary (Cumulative)
Vocab, figures, etc. From chapter 1 until now!
Location with no size, named with a capital letter.
Straight path with no thickness & extends forever, named with 2 points and a symbol above or a cursive letter.
Flat surface with no thickness and extends forever, named with 3 non-collinear points or a cursive capital letter.
Points on the same line.
Points NOT on the same line.
Part of a line consisting of 2 points and everything in between, named with the 2 endpoints and a symbol above.
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.
Two rays that have a common endpoint and form a line.
Statement that is accepted as true without proof.
Absolute value of the difference of the coordinates of two points.
Segments that have the same length, marked with tick marks.
Way of creating a figure that is more precise, using a compass, straightedge, etc.
The point that divides a segment into two congruent segments.
To divide something in half.
Any ray, segment, or line that intersects a segment at its midpoint.
Figure formed by 2 rays with a common endpoint.
1/360 of a circle.
Angle less than 90, but greater than 0.
90 degree angle.
Angle greater than 90, but less than 180.
180 degree angle.
Angles with the same degree measure.
A ray that divides an angle into two congruent angles.
Angles that share a common endpoint and a common side.
Pair of adjacent angles that form a line.
2 angles whose measures add to 90 degrees.
2 angles whose measures add to 180 degrees.
2 angles across from each other in an "X" (non-adjacent)
Sum of the side lengths of a figure (or distance around a figure).
number of non-overlapping square units of a given size that exactly cover a figure.
Segment that passes through the center of a circle and whose endpoints are on the circle.
Segment whose endpoints are the center of the circle and a point on the circle.
The ratio of a circle's circumference to its diameter.
The side of a triangle across from the right angle (the longest side).
( (X1+X2)/2 , (Y1+Y2)/2 )
Sqrt( (X2-X1)^2 + (Y2-Y1)^2 )
Change in position, size, or shape of a figure.
The original figure.
The new figure.
Transformation across a line.
Transformation about a point.
Transformation in which all points move the same distance in the same direction.
The coolest teacher ever!
The process of reasoning that a rule or statment is true because specific cases are true.
A statement you believe to be true based on inductive reasoning.
An example that shows a conjecture is not true.
If p, then q.
If q, then p.
If not p, then not q.
If not q, then not p.
Logically equivalent statements
Statements that have the same truth value. (Conditional & Contrapositive) (Converse & Inverse)
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.
p if and only if q.
Closed plane figure formed by three or more line segments.
3 sided polygon.
4 sided polygon.
An argument that uses logic, definitions, properties, and previously proven statements to show that a conclusion is true.
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.
Proof which uses boxes and arrows to show the structure of the proof.
Proof that presents the steps & reasons of a proof as sentences in a paragraph.
Coplanar lines that do not intersect.
Lines that intersect at 90 degree angles.
Lines that are noncoplanar, are not parallel, and do not intersect.
Planes that do not intersect.
A line that intersects two coplanar lines at two different points.
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.
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.
Rise/Run. (Y2 - Y1) / (X2 - X1).
Y - Y1 = m(X - X1)
y = mx+b
Equation of a Horizontal Line
y = a
Equation of a Vertical Line
x = a
Same slope, different y-intercept.
Same slope, same y-intercept.
triangle with 3 acute angles
triangle with 3 congruent angles
triangle with 1 right angle
triangle with 1 obtuse angle
triangle with 3 congruent sides
triangle with at least 2 congruent sides
triangle with no congruent sides
line added to a figure to aid in a proof
theorem whose proof follows directly from another theorem
set of all points inside a figure
set of all points outside a figure
an angle formed by two sides of a triangle
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
polygons with congruent corresponding angles and sides (same size and same shape)
an angle formed by 2 adjacent sides of a polygon
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
style of proof that uses coordinate geometry and algebra
an angle formed by the 2 legs of an isosceles triangle
angles formed by a leg and the base of an isosceles triangle
when a point is the same distance from 2 or more objects
set of points that satisfies a given condition
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
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
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
type of proof which begins by assuming the conclusion is false and seeks to reach a contradiction
a set of 3 nonzero whole numbers a, b, and c, such that a^2+b^2=c^2
a segment that connects any two nonconsecutive vertices of a polygon
polygon that is both equilateral and equiangular
a polygon with any part of a diagonal containing points in the exterior of the polygon
a polygon where no diagonals are in the exterior
a quadrilateral with two pairs of parallel sides
a quadrilateral with four right angles
a quadrilateral with four congruent sides
a quadrilateral with four right angles and four congruent sides
a quadrilateral with exactly two pairs of congruent consecutive sides
a quadrilateral with exactly one pair of parallel sides
a trapezoid in which the two legs are congruent
Midsegment of a Trapezoid
segment whose endpoints are midpoints of the legs of a trapezoid
comparison of two numbers by division
equation stating that two ratios are equal
the product of the extremes ad and the product of the means bc
figures that have the same shape but not necessarily the same size
polygons with congruent corresponding angles and proportional corresponding side lengths
ratio of the lengths of the corresponding sides of two similar polygons
any method that uses formulas, similar figures, and/or proportions to measure an object
represents an object as smaller or larger than its actual size
the ratio of any length in a drawing to the corresponding actual length
transformation that changes the size of a figure but not its shape
describes how much a figure is enlarged or reduced
the square root of a product of two numbers
ratio of two sides of a triangle
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
quantity with both magnitude and direction
lists the horizontal and vertical change of a vector
length of a vector
angle a vector makes with a horizontal line
have the same magnitude and direction
have the same or opposite directions
sum of two vectors
Area of a Parallelogram
Area of a Triangle
Area of a Trapezoid
Area of a Rhombus/Kite
Area of a Circle
Circumference of a Circle
Area of a Regular Polygon
is made up of simple shapes, such as triangles, rectangles, and trapezoids
The probability of an event based on a ratio of geometric measures such as length or area
flat surface of a 3D figure
where two faces intersect on a 3D figure
where three or more faces intersect on a 3D figure
formed by two parallel congruent polygonal faces connected by parallelograms
formed by two parallel congruent circle bases connected by a curved surface
formed by a polygonal base and triangular faces that meet at a vertex
formed by a circular base and a curved surface that connects the base to the vertex
diagram of the surfaces of a 3D figure that can be folded to form it
shows 6 different views of an object: front, back, right, left, top, bottom
way to show three sides of a figure from a corner view
way to show depth to a figure by drawing things that are farther away smaller
formed by four or more polygons that intersect only at the edges
set of all points in 3D
the total area of all faces and curved surfaces of a 3D figure
sum of the areas of the lateral faces of a 3D figure
the number of nonoverlapping unit cubes that will exactly fill the interior of a 3D figure
locus of points in spaces that are a fixed distance from a given point called the center
half a sphere
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
segment whose endpoints lie on a circle
line that intersects a circle at 2 points
line that intersects a circle at one point
circles with the same radii
coplanar circles with the same center
coplanar circles that intersect at one point
an angle whose vertex is the center of a circle
an unbroken part of a circle consisting of two points and all points between them
half of a circle
arcs of the same circle that intersect at exactly one point
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
distance along an arc, measured in linear units
an angle whose vertex is on a circle and whose sides contain chords of the circle
consists of endpoints that lie on the sides of an inscribed angle and all points between them
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
segment of a tangent with one endpoint on the circle
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