The Basic Building Blocks of Geometry

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The Basic Building Blocks of Geometry
B
C
A
x
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Properties of Polygons
Polygon means many angled, is a closed figure
formed by line segments ( no curves are allowed)
Polygons
Not polygons
Convex polygons all angles point outwards
Concave polygons one or pore angles point
inwards
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Naming Polygons Start at one point and follow
all the way around the figure. You may go
clockwise or counter clockwise.
F
A
D
Possible names ABCDF, BCDFA, FDCBA
B
C
of Sides Polygon Name 3 triangle 4 quadrilat
eral 5. pentagon 6 hexagon 7
heptagon 8 octagon 9 nonagon 10 decagon
Pentagon Nonagon
Quadrilateral Octagon
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Types of Angles
B

1
A


C
The vertex is A. The sides are ray AB and ray
AC.
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Acute
Right
Obtuse
Straight
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Complimentary angles- angles when added together
have a degree measurement of 90. Supplementary
angles- angles when added together have a degree
measurement of 180
supplementary
Complimentary
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Find The Missing Angle
Complimentary
x
x
45
30
Supplementary
x
55
45
x
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• Name three acute angles.
• Name three obtuse angles.
• Name two straight angles.
• An angle with a measure of 90 is a _________
  angle.
• An angle with a measure of 110 is a _________
  angle.
• An angle with a measure of 19 is a _________
  angle.
• An angle with a measure of 34 is a _________
  angle.
• An angle with a measure of 150 is a _________
  angle.
• An angle with a measure of 91 is a _________
  angle.
• An angle with a measure of 45 is a _________
  angle.
• An angle with a measure of 89 is a _________
  angle.
• An angle with a measure of 8 is a _________
  angle.

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Types of Triangles
3
5
3
4
3
3
2
3
2
Scalene No congruent sides
Equilateral Triangle 3 sides
Isosceles Triangle 2 Sides
Congruent - means equal to or the same , symbol
for congruent is
Acute 3 acute angles
Equiangular 3 angles
Obtuse Triangle 1 Obtuse angle
Right Triangle 1 90 angle
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Finding the Measures of a Triangles Angles
The sum of the interior angles of a triangle is
180
40 50 90 180
60 60 60 180
Finding missing angles subtract what angles
you have been given from 180.
Angle sum of a quadrilateral is 360º !
90 90 90 90 360
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Parallel lines- ( ll )have the same slope,
never cross Perpendicular lines ( )
have opposite slopes. Cross at exactly
90 Intersecting lines- lines that
cross Vertical angles- angles that are directly
opposite from each other, and have the same angle
measurement.
C
D


B

ABC and EBD are vertical angles.
CBD and ABE are vertical angles.

A
E

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Adjacent angles angles that are side by side.
They share a common ray. They are supplementary
ABC and CBD are adjacent angles.
C
D


B


A
E

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Working With Lines
Intersecting lines- Lines that cross Point of
Intersection- Point where lines cross Transversal
a line that intersects 2 or more lines in
different places Perpendicular line a line that
intersects at exactly 90, is the symbol,
can be a transversal
T
Transversals
Lines b, c, d, are transversals. The cross 2 or
more lines. Line a is not a transversal because
it crosses at a point of intersection.
f
g
h
Which Lines are Transversals? Answer e, g, h
Line f is not because it only crosses at a point
of intersection
e
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Angles Formed By Parallel Lines and a Transversal
Alternate Interior angles inside angles on
opposite sides of a transversal are congruent (
equal)
Corresponding angles- angles that appear to be in
the same spot in relation to the parallel lines.
These lines are also congruent.
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Same-Side Interior angles are supplementary
(equal to 180)

Opposite angles- angles that are opposite from
each other. Are congruent ( equal)
1 4 are congruent 3 2
are congruent 5 8 are congruent
7 6 are congruent
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Alternate Exterior angles outside side angles
on opposite sides of a transversal are congruent
( equal)
Circular angles a circular angle is equal to
360º.
360º -45º 315º X 315º
45º
x
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Pythagorean Theorem
Hypotenuse side opposite the 90 angle Leg
side of a triangle that is not the hypotenuse
Pythagorean Theorem - a2 b2 c2
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b
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