Non-Euclidean geometry | Foundations of geometry | History of geometry | Elementary geometry
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles. This postulate does not specifically talk about parallel lines; it is only a postulate related to parallelism. Euclid gave the definition of parallel lines in Book I, Definition 23 just before the five postulates. Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate. The postulate was long considered to be obvious or inevitable, but proofs were elusive. Eventually, it was discovered that inverting the postulate gave valid, albeit different geometries. A geometry where the parallel postulate does not hold is known as a non-Euclidean geometry. Geometry that is independent of Euclid's fifth postulate (i.e., only assumes the modern equivalent of the first four postulates) is known as absolute geometry (or sometimes "neutral geometry"). (Wikipedia).
Geometry - Ch. 4: Lines and Angles (2 of 37) Postulates of Parallel and Perpendicular Lines
Visit http://ilectureonline.com for more math and science lectures! In this video I will define and explain postulates of parallel and perpendicular lines. 1) If there is a line and a point not on the line then there is exactly one line through the point PARALLEL to the initial line. 2) I
From playlist GEOMETRY CH 4 LINES AND ANGLES
This video states the parallel line postulate and shows how to construct parallel lines. http://mathispower4u.wordpress.com/
From playlist Parallel and Perpendicular Lines
Proving Parallel Lines with Angle Relationships
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
This video states the perpendicular line postulate and shows how to construct a perpendicular line. http://mathispower4u.wordpress.com/
From playlist Parallel and Perpendicular Lines
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👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
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👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
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http://www.youtube.com/vinteachesmath This video focuses on the angles formed from parallel lines and transversals. In particular, the corresponding angles and straight angle postulate is utilized in this video. This video is appropriate for a student taking a course in Geometry. Stude
From playlist Geometry
What are the Angle Relationships for Parallel Lines and a Transversal
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
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👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
The Beautiful Story of Non-Euclidean Geometry
Visit https://brilliant.org/TreforBazett/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations â–ºhttps://www.beautifulequation.com/pages/trefor In this vi
From playlist Cool Math Series
Triangle Similarity - AA SSS SAS & AAA Postulates, Proving Similar Triangles, Two Column Proofs
This geometry video tutorial provides a basic introduction into triangle similarity. it explains how to use two column proofs in order to prove if two triangles are similar using the mostly the AA postulates. Other triangle similarity postulates mentioned are the AAA, SSS, and SAS postul
From playlist Geometry Video Playlist
Geometry - Ch. 4: Lines and Angles (30 of TBD) Parallel Lines and Corresponding Angles
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn 2 postulates on parallel lines and corresponding angles. Postulate: If 2 lines are cut by a transversal so that the cor
From playlist GEOMETRY CH 4 LINES AND ANGLES
Euclid's puzzling parallel postulate - Jeff Dekofsky
View full lesson: http://ed.ted.com/lessons/euclid-s-puzzling-parallel-postulate-jeff-dekofsky Euclid, known as the "Father of Geometry," developed several of modern geometry's most enduring theorems--but what can we make of his mysterious fifth postulate, the parallel postulate? Jeff Dek
From playlist Even More TED-Ed Originals
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What is distinctly human about breaking the rules? And why does that matter for creative thinking, mathematics, and AI? Watch Junaid's full talk here: https://youtu.be/i2trJEIFIvY Subscribe for regular science videos: http://bit.ly/RiSubscRibe Junaid is a mathematician turned educator.
From playlist Mathematics
This video tutorial provides a basic introduction into geometry. My E-Book: https://amzn.to/3B9c08z Video Playlists: https://www.video-tutor.net Homework Help: https://bit.ly/Find-A-Tutor Subscribe: https://bit.ly/37WGgXl Support & Donations: https://www.patreon.com/MathScienceTuto
From playlist Geometry Video Playlist
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"What is mathematics?" and "What do mathematicians do?" Mathematics seems daunting or deeply nerdy. In my view, it's another way to look at the world, the same as art or science. Let's do some mathematics ourselves, speeding through the process from asking a question to telling others what
From playlist Summer of Math Exposition 2 videos
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From playlist Common Core Standards - 8th Grade
How To Determine If Two Lines are Parallel to Apply Angle Theorems
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
This seminar covers the Fifth Postulate, Propositions 29 and 30 of Euclid's Elements, presented by Kenneth Chan and Daniel Murfet. You can join this seminar from anywhere, on any device, at https://www.metauni.org. This video was recorded in The Rising Sea (https://www.roblox.com/games/8
From playlist Euclid