topic - Chandler Unified School District
... ALGEBRA SKILLS 2: SLOPE review 2.4 Mathematical Modeling S4C1PO3 Create & analyze inductive and deductive arguments concerning geometric ideas & relationships. 2.5 Angle Relationships S4C1PO4 Apply properties, theorems, & constructions about parallel lines, perpendicular lines & angles to prove theo ...
... ALGEBRA SKILLS 2: SLOPE review 2.4 Mathematical Modeling S4C1PO3 Create & analyze inductive and deductive arguments concerning geometric ideas & relationships. 2.5 Angle Relationships S4C1PO4 Apply properties, theorems, & constructions about parallel lines, perpendicular lines & angles to prove theo ...
3. The parallel axiom Axiom 8 (Parallel Axiom). Given a line k, and a
... We remark that the point of the axiom is not the existence of the parallel, but the uniqueness. We will see below that existence actually follows from what we already know. It is sometimes convenient to think of a line as being parallel to itself, so we make the following formal definition. Two line ...
... We remark that the point of the axiom is not the existence of the parallel, but the uniqueness. We will see below that existence actually follows from what we already know. It is sometimes convenient to think of a line as being parallel to itself, so we make the following formal definition. Two line ...
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... Many teachers and textbooks treat congruence as “same size, same shape”. This is not sufficient to transition from middle school to high school geometry. The key to grade specific rigor (informal to increased formalism) in CCSS is the transformational approach. Transformations (rigid motions + dilat ...
... Many teachers and textbooks treat congruence as “same size, same shape”. This is not sufficient to transition from middle school to high school geometry. The key to grade specific rigor (informal to increased formalism) in CCSS is the transformational approach. Transformations (rigid motions + dilat ...
Description of Standards_Cambridge.xlsx
... *Cut a triangle with a midsegment and show that both triangles are similar using AA • Prove that if two triangles are similar, then the ratio of corresponding altitudes is equal to the ratio of corresponding sides. • To prove the Pythagorean theorem using triangle similarity See picture We can cut a ...
... *Cut a triangle with a midsegment and show that both triangles are similar using AA • Prove that if two triangles are similar, then the ratio of corresponding altitudes is equal to the ratio of corresponding sides. • To prove the Pythagorean theorem using triangle similarity See picture We can cut a ...
History of geometry
Geometry (from the Ancient Greek: γεωμετρία; geo- ""earth"", -metron ""measurement"") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic).Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See Areas of mathematics and Algebraic geometry.)