Geometry

TR

________ is bisected by segment AB, creating two congruent segments: PT and PR.

Circle

________: The set of all points in a plane that are a given distance away from a given point called the center.

Midpoint

________: A point on a line segment that is equidistant from the two endpoints.

Conjecture

________: A statement though to be true but not yet proved true or false.

Ray

________: Part of a line that has one endpoint and extends indefinitely in one direction (A; point B in between the arrow and the endpoint.

Euclid

________ (Lived in Alexandria around 300 BCE)

Angle

________: Formed by two rays that meet at a common endpoint.

Protractor

________: Tool used to measure an angle in degrees.

Label

________: italicized m (or lowercase letter)/two points on a line and mark them with PQ (one- dimensional)

Euclidean geometry

There are some concepts in ________ that are considered undefinable, but are used to define other foundational objects.

Collinear

________: Points that lie on the same line.

Linear pair

________: Two adjacent angles whose noncommon sides are opposite rays.

Coplanar

________: Contained within the same plane.

AB

Line segment: Portion of a line with two endpoints ________ (Line on top without arrows)

Postulate

________: A statement accepted without proof; also known as an axiom.

Complementary angles

________ are two angles whose measures have a sum of 90.

Protractor postulate

________: Given any angle, we can express its measure as a unique positive number from 0 to 180 degrees.

Theorem

________: A statement that has been proven based on previous theorems, postulates, or axioms.

Linear pair postulate

________: If two angles form a linear pair, then they are supplementary.

Midpoint theorem

________: If P is the midpoint of TR, then PT (congruent symbol) PR.

parallel lines

No intersection: Called ________.

Linear pair

________: Two adjacent angles whose noncommon sides are opposite rays.

Reflexive property

________: The property that states that for any real number x, x= x; or that a figure and its parts (e.g., sides, angles, triangles, etc .)

Vertical angles

________ are opposite (nonadjacent) angles formed by two intersecting lines.

deductive reasoning

An argument using ________ and justification of steps in a logical order.

Rays

________ are part of a line so one could start at D and extend through E; ________ DE.

protractor

A(n) ________ is a tool used to measure an angle in degrees.

Angle

________: A figure formed by two rays that share a common endpoint.

AB

________= CD and EF= CD (________ equals the length of CD, EF equals the length of CD)

Deductive reasoning

________: The process of utilizing facts, properties, definitions, and theorems to form a logical argument.

-Collinear

Points that lie on the same line

-Coplanar

Contained within the same plane

-Deductive reasoning

The process of utilizing facts, properties, definitions, and theorems to form a logical argument

-Postulate

A statement accepted without proof; also known as an axiom

-Theorem

A statement that has been proven based on previous theorems, postulates, or axioms

-Label

P

-Label

italicized m(or lowercase letter) / two points on a line and mark them with PQ(one-dimensional)

-Label

Script/uppercase italicized letter

Point existence postulate for lines

A line contains at least two points

Unique line postulate

Through any two points there exists one and only one line

Point existence postulate for places

A plane contains at least three noncollinear points

Unique plane postulate

Through any three noncollinear points there exists one and only one plane

Flat plane postulate

If two point are in a plane, then the line that contains those two points lies entirely in that plane

One intersection

Two lines forming an X shape, making one intersection

No intersection

Called parallel lines

-Angle

A figure formed by two rays that share a common endpoint

-Circle

The set of all points in a plane that are a given distance away from a given point called the center

-Line segment

A part of a line that has two endpoints and a specific length(CD and DC both work)

-Parallel lines

Lines that lie in the same plane and do not intersect

-Perpendicular lines

Lines that intersect to form right, or 90-degree, angles

-Ray

Part of a line that has one endpoint and extends indefinitely in one direction(A; point B in between the arrow and the endpoint

-Point

Locations

-Line

AB(Line with another line on top with arrows on each end), or lowercase letters

-Line segment

Portion of a line with two endpoints AB(Line on top without arrows)

-Ray

One endpoint

-Angle

Formed by two rays that meet at a common endpoint

-Ruler postulate

The distance between any two points can be measured by finding the absolute value of the difference of the coordinates representing the points

-Acute angle

An angle measuring between 0 and 90 degrees

-Adjacent angles

Two angles within the same plane that share a common side and vertex, but do not share any common interior points

-Bisect

To divide into two congruent parts

-Congruent angles

Two angles that have the same measure

-Congruent segments

Two lines segments that have the same length

-Midpoint

A point on a line segment that is equidistant from the two endpoints

-Obtuse angle

An angle measuring greater than 90 degrees, but less than 180 degrees

-Protractor

Tool used to measure an angle in degrees

-Right angle

An angle in exactly 90 degrees

-Straight angle

An angle whose measure is exactly 180 degrees

-Reflex angle

An angle whose measures are strictly greater than 180 degrees but less than 360 degrees

ST = 2x

3

TR is bisected by segment AB, creating two congruent segments

PT and PR

Midpoint theorem

If P is the midpoint of TR, then PT (congruent symbol) PR

Protractor postulate

Given any angle, we can express its measure as a unique positive number from 0 to 180 degrees

(After measuring, symbolize it

m

-Conjecture

A statement though to be true but not yet proved true or false

-Deductive reasoning

The process of utilizing facts, properties, definitions, and theorems to form a logical argument

-Reflexive property

The property that states that for any real number x, x = x; or that a figure and its parts (e.g., sides, angles, triangles, etc.)

-Substitution property

The property stating that if two values are equal, then they are interchangeable in an equation; or if two figures are congruent, then they are interchangeable in a statement

-Symmetric property

The property that states that the left and right sides of an equation or congruence statement are interchangeable

-Transitive property

The property states that for all real numbers

-

Deductive reasoning

The process of utilizing facts, properties, definitions, and theorems to form a logical argument

Given

AB = CD and EF = CD

Prove

AB = EF

Prove

AB = EF

-Adjacent angles

Two coplanar angles with a common side, a common vertex, and no common interior points

-Congruent angles

Two angles that have the same measure

-Linear pair

Two adjacent angles whose noncommon sides are opposite rays

-Vertical angles

Opposite angles formed by two intersecting lines

-Complementary angles

Two angles whose measures have a sum of 90 degrees

-Linear pair

Two adjacent angles whose noncommon sides are opposite rays

-Opposite rays

Rays that are collinear and have the same endpoint but run infinitely in opposite directions

-Supplementary angles

Two angles whose measures have a sum of 180 degrees

Linear pair postulate

If two angles form a linear pair, then they are supplementary

Congruent supplements theorem

If two angles are supplements of the same angle or of congruent angles, then the two angles are congruent