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 | One-dimensional set of infinite points | Two-dimensional 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 90-degree, 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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