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Number of Sides
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Name of Polygon
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|
3
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Triangle
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|
4
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Quadrilateral
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|
5
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Pentagon
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|
6
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Hexagon
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7
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Heptagon
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8
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Octagon
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|
9
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Nonagon
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|
10
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Decagon
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|
12
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Dodecagon
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|
n
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n-gon
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Term
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Definition
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Vertex of the polygon
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The common endpoint of two sides of a polygon
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Diagonal
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A segment connecting any two nonconsecutive vertices of a polygon
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Regular polygon
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An equilateral and equiangular polygon (always convex)
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Concave polygon
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A polygon with parts of a diagonal on the exterior of the polygon
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Convex polygon
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A polygon with every part of the diagonals on the interior
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Rectangle
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A quadrilateral with four right angles
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Rhombus
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A quadrilateral with four congruent sides
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Square
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A quadrilateral with four right angles and four congruent sides; it is a parallelogram, a rectangle, and a rhombus
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Kite
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A quadrilateral with exactly two pairs of consecutive sides
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Trapezoid
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A quadrilateral with exactly one pair of parallel sides
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Base
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One of the parallel sides of a trapezoid
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Leg
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One of the nonparallel sides of a trapezoid
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Isosceles trapezoid
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A trapezoid in which the legs are congruent
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Midsegment of a trapezoid
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The segment whose endpoints are the midpoints of the legs of a trapezoid
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Name
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Theorem
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Polygon angle sum theorem
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The sum of the interior angle measures of a convex polygon with n sides is (n - 2)180 degrees.
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Polygon exterior angle sum theorem
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The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360 degrees.
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Trapezoid Midsegment Theorem
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The midsegment of a trapezoid is parallel to each base, and its length is one half the sum of the lengths of the bases
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Name
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Formula
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Sum of interior angle measures
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(n - 2)180
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Midsegment of a trapezoid length
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1/2(base 1 + base 2)
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Midpoint Formula
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(x,y) = [(x1 + x2)/2], [(y1 + y2)/2]
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Distance formula
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√(x2 − x1)2+(y2 − y1)2
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If a quadrilateral is a parallelogram, then...
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Its opposite sides are congruent AND
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Its opposite angles are congruent AND
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Its consecutive angles are supplementary AND
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Its diagonals bisect each other.
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If...
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One pair of opposite sides of a quadrilateral are parallel and congruent OR
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Both pairs of opposite sides of a quadrilateral are congruent OR
|
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Both pairs of opposite angles of a quadrilateral are congruent OR
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An angle of a quadrilateral is supplementary to both of its consecutive angles OR
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The diagonals of a quadrilateral bisect each other,
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then the quadrilateral is a parallelogram.
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If a quadrilateral is a rectangle, then...
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It is a parallelogram AND
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Its diagonals are congruent.
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If a quadrilateral is a rhombus, then...
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It is a parallelogram AND
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Its diagonals are perpendicular AND
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Each diagonal bisects a pair of opposite angles.
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If a quadrilateral is a kite, then...
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Its diagonals are perpendicular AND
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Exactly one pair of opposite angles are congruent.
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If a quadrilateral is an isosceles trapezoid, then...
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Each pair of base angles are congruent AND
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Its diagonals are congruent.
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If...
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A trapezoid has one pair of congruent base angles OR
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A trapezoid has congruent diagonals,
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then the trapezoid is isosceles.
|
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