Lesson 11: Unknown Angle Proofs—Proofs of Known
... Once a theorem has been proved, it can be added to our list of known facts and used in proofs of other theorems. For example, in Lesson 9 we proved that vertical angles are of equal measure, and we know (from earlier grades and by paper cutting and folding) that if a transversal intersects two paral ...
... Once a theorem has been proved, it can be added to our list of known facts and used in proofs of other theorems. For example, in Lesson 9 we proved that vertical angles are of equal measure, and we know (from earlier grades and by paper cutting and folding) that if a transversal intersects two paral ...
UNIT 4 - LESSON PLANS Class Geometry Topic U4 – Triangle
... CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; ...
... CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; ...
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.)