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Appendix B - 1
Appendix BGEOMETRY FACTS AND THEOREMS
Corresponding Angle Theorem:
When a transversal intersects two parallel lines,the
corresponding angles are equal.
d
c
e
g
h
f
a
b
a = b
c = d
e = g
f = h
A p p e n d i x B : G e o m e t r y F a c t s a n d T h e o r e
m s
Alternate Angle Theorem:
When a transversal intersects two parallel lines,the alternate
angles are equal.
b
a
d
c a = b
c = d
b
a
y
x x + y = 180
a + b = 180
Interior Angle Theorem:
When a transversal intersects two parallel lines,the interior
angles add to 180 (are supplementary.)
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Appendix B - 2
Appendix B GEOMETRY FACTS AND THEOREMS
Isosceles Triangle Theorem:
In an isosceles triangle, the base angles are equal.
Triangle Angle Sum Theorem:
The sum of the interior angles of any triangle is 180.
a b
a = b
a + b + c = 180
c
a
b
a + b + c = 360a
c
b
Exterior Angle Sum Theorem
The sum of the exterior angles of any triangle is 360.
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Appendix B - 3
Appendix BGEOMETRY FACTS AND THEOREMS
Converse Theorems
If the opposite sides of a quadrilateral are equal, then they
are also parallel. That is, thequadrilateral is a
parallelogram.
If two alternate angles are equal, then the lines intersected by
the transversal are parallel.
If two corresponding angles are equal, then the lines
intersected by the transversal are parallel.
If two interior angles add to 180, then the lines intersected by
the transversal are parallel.
If the areas of the squares on two sides of a triangle add to
the area of the square on the thirdside, then the triangle is a
right triangle.
area 1
area 2
area 1+
area 2
Pythagorean Theorem:
In a right triangle, the area of the square on the hypotenuseis
equal to the sum of the areas of the squares on the other
two sides.
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Appendix B - 4
Appendix B GEOMETRY FACTS AND THEOREMS
Other Theorems and Facts
Each angle in an equilateraltriangle is 60.
The sum of the interiorangles of any quadrilateralis 360.
For any polygon, the number of sides= the number of
interiorangles(or vertices).
The sum of the exteriorangles of any polygon is 360.
a
d
b
c
a + b + c + d = 360
60
60
60
a + b + c + d + e + f = 360
a
bd
c
f
e
1
32
4
6
57
7
31 2
4
5
6
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Appendix B - 5
Appendix BGEOMETRY FACTS AND THEOREMS
The sum of the interiorangles of any polygon can be found by
dividing the polygon into non-overlapping triangles. Each triangle
contributes 180.The sum of interior angles = the number of
triangles x180.
The number of non-overlapping triangles = number of sides 2
For a regular polygon,
Each interior angle = the sum of the interior angles number of
angles (or sides).
The perpendicular distance between two parallel lines is the
same no matter where you are on thelines.
In similar triangles, the angles in one triangle equalmatching
angles in the other.However, the sides of one triangle are
multiplesof matching sides of the other.
If the three sides of one triangle equal the three sides of
another triangle then they are congruenttriangles. The angles of
one triangle will equal the corresponding angles of the other
triangle.
a + b + c + d + e + f = (4 triangles)x 180 = 720
a
b
c
d
e
f 1 2
3
4
