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Chapter 6

Polygons, Parallelograms, Rhombi, Squares, Kites, Trapezoids

TermDefinition
Rectangle parallelogram with four right angles
Properties of a Rectangle opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other; diagonals are congruent, opposite sides are parallel, 4 right angles
Rhombus Rhombus is a parallelogram with 4 congruent sides
Properties of a Rhombus opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other; diagonals are perpendicular; diagonals bisect each pair of opposite angles. DIAGONALS ARE NOT CONGRUENT
Properties of a Square opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other; diagonals are congruent; diagonals are perpendicular; diagonals bisect each pair of opposite angles.
Trapezoid a quadrilateral with exactly one pair of parallel sides
isosceles trapezoid trapezoid whose nonparallel sides are congruent
Properties of a Trapezoid angles along the leg add to 180 degrees; all four angles add to 360 degrees; if the trapezoid is isosceles, then the base angles are equal and the diagonals are congruent.
Kite a kite is a quadrilateral with two pairs of consecutive sides congruent and NO opposite sides congruent. A kite has NO parallel sides, so a kite is NOT a parallelogram.
Properties of a Kite all four angles add up to 360 degrees; diagonals are perpendicular; one pair of opposite angles are congruent; no parallel sides. At the short diagonal, the angles are congruent. At the long diagonal, the diagonals are bisected.
Trapezoid Midsegment Theorem The midsegment of a trapezoid is parallel to each base and its measure is one half the sum of the lengths of the bases. M=1/2 (base one + base two)
Polygons a closed figure that has vertices, sides, angles and exterior angles.
How do you name a polygon? By listing the vertices in order around the polygon.
Diagonal a segment connecting 2 nonconsecutive vertices of a polygon.
Convex polygon polygon where NO diagonal goes outside the figure
Concave polygon Polygons where ANY diagonal goes outside the figure. Concave polygons "cave" in.
3 sided polygon triangle
4 sided polygon quadrilateral
5 sided polygon pentagon
6 sided polygon hexagon
7 sided polygon heptagon
8 sided polygon octagon
9 sided polygon nonagon
10 sided polygon decagon
12 sided polygon dodecagon
angle sums of polygons number of triangles formed by diagonals from one vertex
interior angle sum theorem the sum of the measures of the angles in a convex polygon with n sides is (n-2)180
exterior angle sum theorem the sum of the measures of the exterior angles of ANY convex polygon, one at each vertex is 360.
regular polygons a polygon that is BOTH equilateral and equiangular. IF you see the word regular with a polygon, you can divide by the number of sides to find the individual angle measures.
Parallelogram a quadrilateral with BOTH pairs of opposite sides parallel. Abbreviation: //gram
Properties of Parallelograms opposite sides are congruent; opposite angles are congruent; consecutive angles are supplementary; diagonals bisect each other.
Theorem 6.9 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.10 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Theorem 6.11 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a //gram.
Theorem 6.12 If one pair of opposite sides of a quadrilateral is BOTH congruent AND parallel, then the quadrilateral is a //gram.
Created by: amgeometry