Studied by 23 peopleTR
________ 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