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February 07, 2017 Grade 7 Mod 3 Lesson 10-11 Geometry Definitions and History February 07, 2017 What comes to mind when you think of Geometry? February 07, 2017 Geometry began with a practical need to measure shapes. The word geometry means to “measure the earth” and is the science of shape and size of things. Geometry = "measure the earth" February 07, 2017 Egypt It is believed that geometry first became important when an Egyptian pharaoh wanted to tax farmers who raised crops along the Nile River. To compute the correct amount of tax the pharaoh’s agents had to be able to measure the amount of land being cultivated. February 07, 2017 Egyptians and Babylonians Around 2900 BC the first Egyptian pyramid was constructed. Knowledge of geometry was essential for building pyramids, which consisted of a square base and triangular faces. The earliest record of a formula for calculating the area of a triangle dates back to 2000 BC. The Egyptians (5000–500 BC) and the Babylonians (4000–500 BC) developed practical geometry to solve everyday problems, but there is no evidence that they logically deduced geometric facts from basic principles. February 07, 2017 Chinese In early times the focus was on astronomy and perfecting the calendar and not on establishing the proof. Many works simply listed equations or gave diagrams where a proof was hinted at rather than shown. In other cases a proof was shown but it was declared to be an established method after some fashion. February 07, 2017 Greeks It was the early Greeks (600 BC–400 AD) that developed the principles of modern geometry beginning with Thales of Miletus (624–547 BC). Thales is credited with bringing the science of geometry from Egypt to Greece. Thales studied similar triangles and wrote the proof that corresponding sides of similar triangles are in proportion. February 07, 2017 Who is one of the most famous Greek Mathematicians? Pythagoras The next great Greek geometer was Pythagoras (569–475 BC). Pythagoras is regarded as the first pure mathematician to logically deduce geometric facts from basic principles. Pythagoras founded a brotherhood called the Pythagoreans, who pursued knowledge in mathematics, science, and philosophy. Some people regard the Pythagorean School as the birthplace of reason and logical thought. The most famous and useful contribution of the Pythagoreans was the Pythagorean Theorem. The theory states that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse. February 07, 2017 Can you name another famous Greek mathematition? Euclid Euclid of Alexandria (325–265 BC) was one of the greatest of all the Greek geometers and is considered by many to be the “father of modern geometry”. Euclid is best known for his 13-book treatise The Elements. The Elements is one of the most important works in history and had a profound impact on the development of Western civilization. February 07, 2017 Euclidean Geometry Euclid began The Elements with just a few basics, 23 definitions, 5 postulates, and 5 common notions or general axioms. An axiom is a statement that is accepted as true. From these basics, he proved his first proposition. Once proof was established for his first proposition, it could then be used as part of the proof of a second proposition, then a third, and on it went. This process is known as the axiomatic approach. Euclid’s Elements form the basis of the modern geometry that is still taught in schools today. February 07, 2017 Undefined Terms Point Line Plane February 07, 2017 Line Segment A I D G B F C E I L K H J February 07, 2017 Euclid's Jealous Friend Hint #1: Hint #2: RAY February 07, 2017 Point, Line, Plane, Line Segment, Ray February 07, 2017 February 07, 2017 Distance February 07, 2017 Congruent February 07, 2017 Midpoint February 07, 2017 Congruent Segments February 07, 2017 Midpoint and Bisect February 07, 2017 Segment Bisector February 07, 2017 Angle February 07, 2017 February 07, 2017 Angle Measure February 07, 2017 Protractor February 07, 2017 Protractor February 07, 2017 Adjacent, Linear Pair, Vertical Angles February 07, 2017 Complementary and Supplementary Angles February 07, 2017 Rectangle and Square Formulas February 07, 2017 Circle Formulas February 07, 2017 A REGULAR Polygon February 07, 2017 The Midpoint Formula February 07, 2017 The Midpoint Formula February 07, 2017 The Midpoint Formula Find the midpoint February 07, 2017 The Distance Formula February 07, 2017 The Distance Formula February 07, 2017 Transformations February 07, 2017 Transformations February 07, 2017 Homework Page #1 February 07, 2017 Homework Page #2 February 07, 2017 Homework Page #3 February 07, 2017 Homework Page #4 February 07, 2017 Homework Page #5 February 07, 2017 The End