nigra swans

Code: "alternate angles equal to one another" -> Green = Pink "exterior angle" -> Red "exterior angle equal to the interior and opposite angle" -> Red = Pink "sum of the interior angles on the same side" -> Pink + Blue = 180° Arg 1: - Suppose Green > Pink - Then Green + Blue > Pink + Blue - Green + Blue = 2 right angles because line - Therefore Pink + Blue < 2 right angles - By the parallel postulate, the two lines AB and CD meet in the pink/blue direction - We assumed the lines were parallel - Contradiction - Therefore Green = Pink Arg 2: - Green = Red because vertical angles - Therefore Red = Pink - Red + Blue = Pink + Blue - Red + Blue = 2 right angles because straight line - Therefore Pink + Blue = 2 right angles Parallel postulate: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/post5.html Element page: https://mathcs.clarku.edu/~djoyce/java/elements/bookI/propI29.html GeoGebra: https://www.geogebra.org/m/squyduwp Universal Hyperbolic Geometry: https://youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI Euclid Elements playlist: https://odysee.com/@DoctorAjayKumar/ee Greek Math playlist: https://odysee.com/@DoctorAjayKumar/GreekMath Euclid Elements website: https://mathcs.clarku.edu/~djoyce/java/elements/ Where to find me: BitChute: https://www.bitchute.com/doctorajaykumar/ Gab: https://gab.com/DoctorAjayKumar GitLab: https://gitlab.com/DoctorAjayKumar GeoGebra: https://www.geogebra.org/u/doctorajaykumar Odysee (main): https://odysee.com/@DoctorAjayKumar Odysee (podcast): https://odysee.com/@BigBlackCannon Locals: https://orangepill.locals.com/ Minds: https://www.minds.com/doctorajaykumar/ Rumble (main): https://rumble.com/c/c-906055 Rumble (podcast): https://rumble.com/c/c-765395 Twitter: https://twitter.com/DoctorAjayKumar YouTube: https://www.youtube.com/channel/UC3NOwTrjbil7yVghQgJ1mug Website: http://orangepill.healthcare/

Let me know if the new audio is better/worse/same Where to find me: - BitChute: https://www.bitchute.com/doctorajaykumar/ - Gab: https://gab.com/DoctorAjayKumar - GitLab: https://gitlab.com/DoctorAjayKumar - Odysee: https://odysee.com/@DoctorAjayKumar - Locals: https://orangepill.locals.com/ - Minds: https://www.minds.com/doctorajaykumar/ - Rumble (Craig Cannon Clips): https://rumble.com/c/c-765395 - Rumble (Dr. Ajay Kumar PHD): https://rumble.com/c/c-906055 - Twitter: https://twitter.com/DoctorAjayKumar - YouTube: https://www.youtube.com/channel/UC3NOwTrjbil7yVghQgJ1mug - Website: https://orangepill.healthcare/

Artin Algebra link: https://www.amazon.com/Algebra-Micael... Where to find me: - BitChute: https://www.bitchute.com/doctorajayku... - Gab: https://gab.com/DoctorAjayKumar - GitLab: https://gitlab.com/DoctorAjayKumar - Odysee: https://odysee.com/@DoctorAjayKumar - Locals: https://orangepill.locals.com/ - Minds: https://www.minds.com/doctorajaykumar/ - Rumble (Craig Cannon Clips): https://rumble.com/c/c-765395 - Rumble (Dr. Ajay Kumar PHD): https://rumble.com/c/c-906055 - Twitter: https://twitter.com/DoctorAjayKumar - YouTube: https://www.youtube.com/channel/UC3NO... - Website: https://orangepill.healthcare/