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February 07, 2017
Grade 7
Mod 3
Lesson
10-11
Geometry
Definitions and History
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What comes to mind when
you think of Geometry?
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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"
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Undefined Terms
Point
Line
Plane
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Line Segment
A
I
D
G
B
F
C
E
I
L
K
H
J
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Euclid's Jealous Friend
Hint #1:
Hint #2:
RAY
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Point, Line, Plane, Line Segment, Ray
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Distance
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Congruent
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Midpoint
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Congruent Segments
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Midpoint and Bisect
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Segment Bisector
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Angle
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Angle Measure
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Protractor
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Protractor
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Adjacent, Linear Pair, Vertical Angles
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Complementary and Supplementary Angles
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Rectangle and Square Formulas
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Circle Formulas
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A REGULAR Polygon
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The Midpoint Formula
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The Midpoint Formula
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The Midpoint Formula
Find the midpoint
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The Distance Formula
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The Distance Formula
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Transformations
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Transformations
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Homework Page #1
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Homework Page #2
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Homework Page #3
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Homework Page #4
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Homework Page #5
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The End