Euclidean Geometrytheorem  a statement that has been proven based on previous theorems, postulates, or axioms  collinear  points that lie on the same line  deductive reasoning  the process of utilizing facts, properties, definitions, and theorems to form a logical argument  coplanar  contained within the same plane  postulate  a statement accepted without proof; also known as an axiom 
AddEuclidean geometry is comprised of figures and diagrams that can all be constructed using just a straightedge and compass. 
Point, line, planePoint  Line  Plane  No dimensions  Onedimensional set of infinite points  Twodimensional set of all points  Location on coordinate plane designated by an ordered pair (x/y)  Has no beginning or an end  Flat or level surface  Identified with a single capital letter  Identified with a lowercase italicized letter or two capital letters representing two points on the line  Identified with a capital italicized letter 
  Defining termsline segment  a part of a line that has two endpoints and a specific length  ray  part of a line that has one endpoint and extends indefinitely in one direction  circle  the set of all points in a plane that are a given distance away from a given point called the center  angle  a figure formed by two rays that share a common endpoint  parallel lines  lines that lie in the same plane and do not intersect  perpendicularlines  lines that intersect to form right, or 90degree, angles 
Measuring Length and Anglesmidpoint  a point on a line segment that is equidistant from the two endpoints  protractor  tool used to measure an angle in degrees  bisect  to divide into two congruent parts  congruent segments  two line segments that have the same length  Undefined terms:  Point: Points are locations in space. Line: Lines are infinite in two different directions.  Defined terms:  Line segment: A line segment has two endpoints. Ray: Rays have one endpoint. Angle: An angle is formed by two rays with a common endpoint.  adjacent angles  two angles within the same plane that share a common side and vertex, but do not share any common interior points  congruent angles  two angles that have the same measure  obtuse angle  an angle measuring greater than 90 degrees, but less than 180 degrees  straight angle  an angle whose measure is exactly 180 degrees  acute angle  an angle measuring between 0 and 90 degrees  right angle  an angle whose measure is exactly 90 degrees 
  Intro to proofconjecture  a statement thought 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.) are congruent to themselves  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  thepropertythatstatesthattheleftandright sides of an equation or congruence statement are interchangeable  Proofs involve:  given information, in words or a diagram, a statement to be proven, an argument using deductive reasoning and justification of steps in a logical order. A conclusion 
Linear Pairs and Vertical Angleslinear pair  2 adjacentangles whose noncommon sides are opposite rays  vertical angles  opposite angles formed by two intersecting lines 
Complementary and Supplementary Anglesopposite rays  ays 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  complementary angles  angles are two angles whose measures have a sum of 90 degrees 
Example finding angleFind the following angle measures.
𝑚∠1 = ?
𝑚∠1 + 70° = 90°
𝑚∠1 = 90° − 70
𝑚∠1 = 20 

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