Euclidean Geometry
theorem 
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 
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Euclidean geometry is comprised of figures and diagrams that can all be constructed using just a straightedge and compass. 
Point, line, plane
Point 
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 terms
line 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 Angles
midpoint 
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 proof
conjecture 
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 Angles
linear pair 
2 adjacentangles whose noncommon sides are opposite rays 
vertical angles 
opposite angles formed by two intersecting lines 
Complementary and Supplementary Angles
opposite 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 angle
Find the following angle measures.
𝑚∠1 = ?
𝑚∠1 + 70° = 90°
𝑚∠1 = 90° − 70
𝑚∠1 = 20 

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