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=2**pi**r

Area of a Regular Polygon

A=1/2**a**P

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