Transcript Geometry Introduction

geometry
Geometric Applications are
limitless….
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.
There are some geometric principles we
remember…
3600
There are 3600 in every circle.
This initial definition allows for further
angles to be identified
1800
900
450
These are some more common angles
Acute Angles (less than 90O)
A
ABC
B
C
Obtuse Angles (greater than
O)
90
A
ABC
B
C
Acute and Obtuse Angles lead us
into the study of triangles…
Remember:
Interior angles are found
inside a triangle
e
i
Remember:
Exterior angles are found
outside a triangle
i
e
i
e
At this stage, check out the
gizmo…
Supplementary Angles (SAT)
Supplementary Angles must add to 180O
A + B = 180O
A
B
Complementary Angles (CAT)
Complementary Angles must add to 90O
A + B = 90O
A
B
Opposite Angle Theorem (OAT)
If 2 lines intersect, then the
opposite angles are equal.
X
O
O
X
Shape
Theorems
Sum of the Angles of a
Triangle Theorem (SATT)
The sum of the Interior Angles of a
Triangle is 180O
a
b
a + b + c = 180O
c
Isosceles Triangle Theorem
(ITT)
The base angles of an
Isosceles Triangle are equal
Y
X
X
Equilateral Triangle Theorem
(ETT)
X=
X
60O
X
X
Exterior Interior (EI)
An exterior angle equals the sum
of the opposite two interior
angles.
D=A+B
A
B
D
Exterior Angles (EA)
The exterior angles of a triangle
and a quadrilateral sum to 360O
A
B
C
A + B + C = 360O
Sum of the Angles Of a
Quadrilateral Theorem
(SAQT)
The sum of the Interior Angles of a
Quadrilateral is 360O
a + b + c + d = 360O
a
d
b
c
Exterior Angles
The exterior angles of a triangle
and a quadrilateral sum to 360O
A + B + C + D = 360O
D
A
C
B
From the green
workbook
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Page 224
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