Studied by 49 people
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<EFG.)
-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
<ABC
<ABC
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
Note 
Flashcard (48)