geometry geometric applications are limitless…
TRANSCRIPT
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geometry
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Geometric Applications are limitless….
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Geometry
From the Greek words
Geo = earth and metro = measure
The branch of mathematics first popularized in ancient Greek culture by Thales (circa 624-547 BC) dealing with spatial relationships.
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There are some geometric principles we remember…
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3600
There are 3600 in every circle.
This initial definition allows for further angles to be identified
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1800
These are some more common angles
900
450
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Acute Angles (less than 90O)A
B C
ABC
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Obtuse Angles (greater than 90O)A
BC
ABC
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Acute and Obtuse Angles lead us into the study of triangles…
Remember:Interior angles are found
inside a triangle i
i i
Remember:Exterior angles are found
outside a triangle
e
e
e
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At this stage, check out the gizmo…
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Supplementary Angles (SAT)
Supplementary Angles must add to 180O
A + B = 180O
A B
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Complementary Angles (CAT)
Complementary Angles must add to 90O
A + B = 90O
AB
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Opposite Angle Theorem (OAT)If 2 lines intersect, then the
opposite angles are equal.
X XO
O
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Shape Theorems
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Sum of the Angles of a Triangle Theorem (SATT)
The sum of the Interior Angles of a Triangle is 180O
a
b c
a + b + c = 180O
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Isosceles Triangle Theorem(ITT)
X X
The base angles of an Isosceles Triangle are equal
Y
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Equilateral Triangle Theorem(ETT)
X X
XX = 60O
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Exterior Interior (EI)An exterior angle equals the sum of
the opposite two interior angles.
A
BD
D = A + B
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Exterior Angles (EA)The exterior angles of a triangle
and a quadrilateral sum to 360O
A
B
C
A + B + C = 360O
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Sum of the Angles Of a Quadrilateral Theorem
(SAQT)The sum of the Interior Angles of a Quadrilateral is 360O
a
b c
a + b + c + d = 360O
d
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Exterior AnglesThe exterior angles of a triangle
and a quadrilateral sum to 360O
A
B
C
A + B + C + D = 360O
D
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From the green workbook
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