journal 6
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JOURNAL 6. By: Nina Dorion. POLYGON. A polygon is a shape with straight sides, a polygon must have at least four angles and cannot have curved sides or an opened one. Polygon, straight sides. Not a polygon, has curved sides. Not a polygon, has one open side. Convex and concave polygons:. - PowerPoint PPT PresentationTRANSCRIPT
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JOURNAL 6..
By: Nina Dorion
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+ POLYGONA polygon is a shape with straight sides, a polygon must have at least four angles and cannot have curved sides or an opened one
Polygon, straight sides
Not a polygon, has curved sides
Not a polygon, has one open side.
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+Convex and concave polygons:Convex: a polygon that has no angles pointing inwards, no internal angles can be more than 180.
Concave: polygon that has internal angles greater than 180.
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CONVEX CONCAVE
CONCAVE CONVEX
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+EQUILATERAL AND EQUIANGULAR:
equilateral means the sides are congruent
Equiangular means the angles are congruent.
12
12 12
12
Equilateral Equiangular
equilateral
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+INTERIOR ANGLES THEOREM FOR POLYGONS
This theorem is used when you want to find the interior angles of a polygon, to do that you use this formula: (n-2)180
For example:When you have a quadrilateral (four sides) you do the following:(4-2)180 fill in for n
4-2=2(2)180=360360/4=90
Each interior angle must be 900
n
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+Pentagon 5-2=3180x3=540540/5=108Each angle measures 1080
Hexagon 6-2=4180x4=720720/6=120Each angle measures 1200
8-2=6180x6=10801080/8=135Each angle measures 135o
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4 theorems of parallelograms
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+THEOREM:IF A QUADRILATERAL IS A PARALLELOGRAM, THEN ITS OPPOSITE ANGLES ARE CONGRUENT
CONVERSE:IF BOTH PAIRS OF OPPOSITE ANGLES OF A QUADRILATERAL ARE CONGRUENT, THEN THE QUADRILATERAL IS A PARALLELOGRAM.
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+EXAMPLES:
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+THEOREM:If a quadrilateral is a parallelogram then its opposite sides are congruent.
CONVERSE:If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
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+EXAMPLES:
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+THEOREM:If a quadrilateral is a parallelogram, then its diagonals bisect each other
CONVERSE:If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
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+EXAMPLES:
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+THEOREM:If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
CONVERSE:If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram
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45 135
45+135=180
67
113
67+113=180
88
92 88+92=180
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+Prove that a quadrilateral is a parallelogram1. Opposite sides are congruent
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supplementary
5. One set of congruent and parallel sides
6. Opposite sides are parallel
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+ Opposite sides are congruent:
Opposite angles are congruent:
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+Diagonals bisect each other
Consecutive angles are supplementary
a b
M<a+m<b=180
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+One set of congruent parallel sides
Opposite sides are parallel
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+Rectangle:A parallelogram with 4 right angles
Diagonals are congruent
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+Rhombus Parallelogram with 4 congruent sides
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+Square
Parallelogram that is both a rectangle and a rhombus
4 congruent sides and congruent angles Diagonals are congruent and perpendicular
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+quadrilateral
parallelogram
rectangle rhombus
square
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+Trapezoid A quadrilateral with one pair of parallel sides
Isosceles trapezoid: trapezoid with one pair of congruent legs
Properties of isosceles trapezoid:Diagonals are congruentBase angles congruentOpposite angles are supplementary
A
B
M<A+M<B=180
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+base
base
legs
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+Kite has two pairs of congruent adjacent sides•Diagonals are perpendicular•One pair of congruent angles •One of the diagonals bisect the other
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