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Geometry Unit 6 Cheat Sheet by

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
n-gon

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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