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Holt McDougal Geometry Unit 6
Polygons
Number 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 
Vocabulary
Term 
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 & Postulates
Name 
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 


Formulas
Name 
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 Parallelograms
If 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 & Rhombuses
If 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 Trapezoids
If 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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