geometry

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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

900
450
These are some more common angles
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Acute Angles (less than 90O)
A
C
B
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A
C
B
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Acute and Obtuse Angles lead us into the study of
triangles

• Remember
• Interior angles are found inside a triangle

e
i
i
i
e
e
Remember Exterior angles are found outside a
triangle
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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
A
B
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Opposite Angle Theorem (OAT)

• If 2 lines intersect, then the opposite angles
  are equal.

O
X
X
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 180O
a
b
c
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Isosceles Triangle Theorem(ITT)
The base angles of an Isosceles Triangle are equal
Y

• X

X
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Equilateral Triangle Theorem(ETT)
X
X 60O
X
X
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Exterior Interior (EI)

• An exterior angle equals the sum of the opposite
  two interior angles.

D A B
A
B
D
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Exterior Angles (EA)

• The exterior angles of a triangle and a
  quadrilateral sum to 360O

A
A B C 360O
B
C
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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 d 360O
a
d
b
c
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Exterior Angles

• The exterior angles of a triangle and a
  quadrilateral sum to 360O

A B C D 360O
D
A
C
B
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• From the green workbook
• Page 214
• Page 217
• Page 220
• Page 224

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HomeFun YA!!!

• Page 348 1-4
• Page 352 1b, c, d, f, h
• Page 365 1a,c 2a,b