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

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