________ is bisected by segment AB, creating two congruent segments: PT and PR.
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Circle
________: The set of all points in a plane that are a given distance away from a given point called the center.
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Midpoint
________: A point on a line segment that is equidistant from the two endpoints.
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Conjecture
________: A statement though to be true but not yet proved true or false.
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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.
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Euclid
________ (Lived in Alexandria around 300 BCE)
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Angle
________: Formed by two rays that meet at a common endpoint.
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Protractor
________: Tool used to measure an angle in degrees.
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Label
________: italicized m (or lowercase letter)/two points on a line and mark them with PQ (one- dimensional)
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Euclidean geometry
There are some concepts in ________ that are considered undefinable, but are used to define other foundational objects.
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Collinear
________: Points that lie on the same line.
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Linear pair
________: Two adjacent angles whose noncommon sides are opposite rays.
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Coplanar
________: Contained within the same plane.
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AB
Line segment: Portion of a line with two endpoints ________ (Line on top without arrows)
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Postulate
________: A statement accepted without proof; also known as an axiom.
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Complementary angles
________ are two angles whose measures have a sum of 90.
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Protractor postulate
________: Given any angle, we can express its measure as a unique positive number from 0 to 180 degrees.
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Theorem
________: A statement that has been proven based on previous theorems, postulates, or axioms.
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Linear pair postulate
________: If two angles form a linear pair, then they are supplementary.
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Midpoint theorem
________: If P is the midpoint of TR, then PT (congruent symbol) PR.
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parallel lines
No intersection: Called ________.
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Linear pair
________: Two adjacent angles whose noncommon sides are opposite rays.
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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 .)
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Vertical angles
________ are opposite (nonadjacent) angles formed by two intersecting lines.
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deductive reasoning
An argument using ________ and justification of steps in a logical order.
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Rays
________ are part of a line so one could start at D and extend through E; ________ DE.
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protractor
A(n) ________ is a tool used to measure an angle in degrees.
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Angle
________: A figure formed by two rays that share a common endpoint.
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AB
________= CD and EF= CD (________ equals the length of CD, EF equals the length of CD)
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Deductive reasoning
________: The process of utilizing facts, properties, definitions, and theorems to form a logical argument.
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-Collinear
Points that lie on the same line
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-Coplanar
Contained within the same plane
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-Deductive reasoning
The process of utilizing facts, properties, definitions, and theorems to form a logical argument
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-Postulate
A statement accepted without proof; also known as an axiom
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-Theorem
A statement that has been proven based on previous theorems, postulates, or axioms
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-Label
P
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-Label
italicized m(or lowercase letter) / two points on a line and mark them with PQ(one-dimensional)
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-Label
Script/uppercase italicized letter
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Point existence postulate for lines
A line contains at least two points
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Unique line postulate
Through any two points there exists one and only one line
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Point existence postulate for places
A plane contains at least three noncollinear points
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Unique plane postulate
Through any three noncollinear points there exists one and only one plane
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Flat plane postulate
If two point are in a plane, then the line that contains those two points lies entirely in that plane
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One intersection
Two lines forming an X shape, making one intersection
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No intersection
Called parallel lines
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-Angle
A figure formed by two rays that share a common endpoint
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-Circle
The set of all points in a plane that are a given distance away from a given point called the center
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-Line segment
A part of a line that has two endpoints and a specific length(CD and DC both work)
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-Parallel lines
Lines that lie in the same plane and do not intersect
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-Perpendicular lines
Lines that intersect to form right, or 90-degree, angles
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-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
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-Point
Locations
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-Line
AB(Line with another line on top with arrows on each end), or lowercase letters
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-Line segment
Portion of a line with two endpoints AB(Line on top without arrows)
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-Ray
One endpoint
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-Angle
Formed by two rays that meet at a common endpoint
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-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
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-Acute angle
An angle measuring between 0 and 90 degrees
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-Adjacent angles
Two angles within the same plane that share a common side and vertex, but do not share any common interior points
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-Bisect
To divide into two congruent parts
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-Congruent angles
Two angles that have the same measure
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-Congruent segments
Two lines segments that have the same length
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-Midpoint
A point on a line segment that is equidistant from the two endpoints
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-Obtuse angle
An angle measuring greater than 90 degrees, but less than 180 degrees
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-Protractor
Tool used to measure an angle in degrees
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-Right angle
An angle in exactly 90 degrees
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-Straight angle
An angle whose measure is exactly 180 degrees
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-Reflex angle
An angle whose measures are strictly greater than 180 degrees but less than 360 degrees
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ST = 2x
3
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TR is bisected by segment AB, creating two congruent segments
PT and PR
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Midpoint theorem
If P is the midpoint of TR, then PT (congruent symbol) PR
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Protractor postulate
Given any angle, we can express its measure as a unique positive number from 0 to 180 degrees
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(After measuring, symbolize it
m
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-Conjecture
A statement though to be true but not yet proved true or false
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-Deductive reasoning
The process of utilizing facts, properties, definitions, and theorems to form a logical argument
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-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.)
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-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
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-Symmetric property
The property that states that the left and right sides of an equation or congruence statement are interchangeable
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-Transitive property
The property states that for all real numbers
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-
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Deductive reasoning
The process of utilizing facts, properties, definitions, and theorems to form a logical argument
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Given
AB = CD and EF = CD
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Prove
AB = EF
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Prove
AB = EF
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-Adjacent angles
Two coplanar angles with a common side, a common vertex, and no common interior points
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-Congruent angles
Two angles that have the same measure
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-Linear pair
Two adjacent angles whose noncommon sides are opposite rays
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-Vertical angles
Opposite angles formed by two intersecting lines
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-Complementary angles
Two angles whose measures have a sum of 90 degrees
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-Linear pair
Two adjacent angles whose noncommon sides are opposite rays
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-Opposite rays
Rays that are collinear and have the same endpoint but run infinitely in opposite directions
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-Supplementary angles
Two angles whose measures have a sum of 180 degrees
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Linear pair postulate
If two angles form a linear pair, then they are supplementary
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Congruent supplements theorem
If two angles are supplements of the same angle or of congruent angles, then the two angles are congruent
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