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Unit 3
M.Sigley, Baker MS
Unit 3
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Unit 3
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Unit 3
DEFINITION
DEFINITION
Unit 3
Polygon
 Plane figure made of 3 or more line
Equiangular
segments
 All angles congruent
 Line segments are called sides
 Sides have common endpoints called
vertices
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DEFINITION
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DEFINITION
Equilateral
Regular
 All sides congruent
 All angles congruent
 All sides congruent
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n
Ѳ
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DEFINITION
Central Angle
Reflectional Symmetry
 Angle formed using the center of
the polygon
 When a figure can be reflected
across a line and still be the
same picture

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DEFINITION
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Ѳ = 360/n (n = number of sides)
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DEFINITION
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Equilateral Triangle
Isosceles Triangle
 All sides congruent
 Two sides congruent
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DEFINITION
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DEFINITION
Scalene Triangle
Rotational Symmetry
 NO sides congruent
 When a figure moves around a
fixed point and the image
remains the same
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DEFINITION
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PROPERTIES
PROPERTIE
S
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Parallelogram
 Quadrilateral with two pairs of parallel
sides
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Trapezoid
 Opposite sides are congruent
 Quadrilateral with one pair of
parallel sides
 Opposite angles are congruent
 Diagonals bisect each other
 Consecutive angles are supplementary
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PROPERTIES
Rhombus
Rectangle
 Quadrilateral with four congruent
sides
 Quadrilateral with four right angles
 Parallelogram
 Parallelogram
 Diagonals are congruent
 Diagonals are perpendicular
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PROPERTIES
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DEFINITION
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PROPERTIES
Square
Transversal
 Quadrilateral with four right angles
and four congruent sides
 Line, ray, or segment that intersects
two or more coplanar lines, rays or
segments at different points
 Parallelogram, rhombus and rectangle
 Diagonals are congruent, bisect each
other, and are perpendicular
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1
3
4
3
4
6
5
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Alternate Interior Angles?
Corresponding Angles?
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5
7
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Same Side Interior Angles?
Alternate Exterior Angles?
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THEOREM
POSTULATE
Unit 3

1≅
5

4≅
6

2 ≅

3 ≅
5

4≅
8

3≅
7
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THEOREM
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THEOREM
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Same Side Interior Angles
If two parallel lines are cut by a
transversal, then same side interior
angles are supplementary.
m

1≅
7

2 ≅
8
4 + m 5 = 180˚
m 3 + m 6 = 180
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n
n
1
m
2
5
4
3
Measure of an Interior Angle?
Sum of Interior Angles?
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3
2
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THEOREM
Exterior Angle of a Triangle
Triangle Sum
 The measure of the exterior angle of
a triangle is equal to the sum of
the remote interior angles.
 The angles of a triangle added
together equal 180°.
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THEOREM
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THEOREM
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THEOREM
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Measure of Interior Angle of a Polygon
Sum of Interior Angles of a Polygon
m = 180° - 360°/n
s = (n – 2)180°
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Sum
of
Exterior
2
Angles?
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Slope?
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DEFINITION
THEOREM
Unit 3
Midsegment of a Triangle
 A segment whose endpoints are the
midpoints of two sides.
Sum of Exterior Angles of Polygon
360°
 Parallel to a side of the triangle and
has a measure equal to ½ of that
side.
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DEFINITION
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DEFINITION
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Midsegment of a Trapezoid
 A segment whose endpoints are the
midpoints of the non-parallel sides.
Slope
y2 – y1
 Parallel to the bases and has a
measure that is ½ the sum of the
bases.
x2 - x1
midsegment= ½ (base 1 + base 2)
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Midpoint?
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THEOREM
THEOREM
Unit 3
Perpendicular Lines
 Two lines are perpendicular if and
only if they have slopes that are
negative reciprocals.
Parallel Lines
 Two lines are parallel if and only if
they have the same slope.
 The product of the slopes is -1.
(a/b and –b/a)
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FORMULA
Midpoint
x2 + x1
2
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,
y2 + y1
2
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x