Introduction to Geometry: Geometric Systems
- 2. Axiomatic System In mathematics, an axiomatic system has a set of axioms, or rules, that are used to prove other statements or facts. Henry and Emma are playing a ball toss game. To play, Henry and Emma need 1 spinner, 6 balls, 50 tokens, and a ball toss board.
- 3. Rules When you get a ball in a hole, you earn the points associated with that hole. Spin the arrow. When the arrow lands on a number, toss that many balls. You must stand 3 feet away from the board to toss a ball. You get 1 token for every 50 points you earn. 5 6 You cannot earn more than 1000 points during a turn You lose aturn if you spin a 5. You need at least 2 people to play. The first person to earn 2000 points wins. 7 8
- 4. Let's Discuss and Analyze Together Do you think some of the rules contradict each other? Why or why not? First Question Do you think some of the rules are incomplete? Why or why not? Second Question Third Question Which 2 rules contain repetitive information?
- 5. are words , usually readily understood, that are not formally explained by means of more basic words and concepts. Undefined terms Understanding the Lesson Geometry is an axiomatic system based on logical reasoning and axioms. assign properties to a mathematical object. A defined term is a term that has a definition and can be explained using undefined terms and/or defined terms. Definition statements that are accepted as true without proof. Axioms or Postulate statements or conjectures that can be proven true using undefined terms, definitions, and axioms. Theorems
- 6. Example Question 1 In the fictional country of Rythoth, blue animals are from the mountains, and red animals are from the valleys. These animals are categorized into three distinct classes: mammals, birds, and reptiles. Mammals are covered by hair or fur, birds are covered by feathers, and reptiles are covered by scales.
- 8. Types of Geometry Study of geometric figures without the use of coordinates. It is sometimes called pure geometry or Euclidean geometry. Synthetic Geometry Study of geometry using a coordinate system. It is sometimes called coordinate geometry or Cartesian Geometry Analytic Geometry