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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 | n-gon |
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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