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

These are some more common angles

900

450

Acute Angles (less than 90O)A

B C

ABC

Obtuse Angles (greater than 90O)A

BC

ABC

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

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

AB

Opposite Angle Theorem (OAT)If 2 lines intersect, then the

opposite angles are equal.

X XO

O

Shape Theorems

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

Isosceles Triangle Theorem(ITT)

X X

The base angles of an Isosceles Triangle are equal

Y

Equilateral Triangle Theorem(ETT)

X X

XX = 60O

Exterior Interior (EI)An exterior angle equals the sum of

the opposite two interior angles.

A

BD

D = A + B

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

a + b + c + d = 360O

d

Exterior AnglesThe exterior angles of a triangle

and a quadrilateral sum to 360O

A

B

C

A + B + C + D = 360O

D

From the green workbook

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