Chapter 6 Defintions and Theorems

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clairebbboyer  on January 18, 2012

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Chapter 6 Defintions and Theorems

 Diagonala segment that connects any two nonconsecutive vertices of a polygon
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Definitions

Diagonal a segment that connects any two nonconsecutive vertices of a polygon
parallelogram a quadrilateral with both pairs of opposite sides parallel
rectangle a parallelogram with four right angles
rhombus a parallelogram with all four sides congruent
square a parallelogram with four congruent sides and four right angles
trapezoid a quadrilateral with exactly one pair of parallel sides
bases of a trapezoid the parallel sides of a trapezoid
legs of a trapezoid the nonparallel sides of a trapezoid
base angles of a trapezoid formed by the base and one of the legs of a trapezoid
isosceles trapezoid when the legs of a trapezoid are congruent
midsegment of a trapezoid the segment that connects the midpoints of the legs of a trapezoid
kite a quadrilateral with exactly two pairs of consecutive congruent sides
polygon interior angles sum theorem the sum of the interior angle measures of an n-sided convex polygon is (n-2)180
polygon exterior angles sum theorem the sum of the exterior angle measures of a convex polygon, one angle at each vertex, is 360
properties of parallelograms theorem if a quadrilateral is a parallelogram, then its opposite sides are congruent
properties of parallelograms theorem if a quadrilateral is a parallelogram, then its opposite angles are congruent
properties of parallelograms theorem if a quadrilateral is a parallelogram, then its consecutive angles are supplementary
properties of parallelograms theorem if a parallelogram has one right angle, then it has four right angles
diagonals of parallelograms theorem if a quadrilateral is a parallelogram, then its diagonals bisect each other
diagonals of parallelograms theorem if a quadrilateral is a parallelogram, then each diagonal seperates the parallelogram into two congruent triangles
conditions for parallelograms theorem if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
conditions for parallelograms theorem if both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram
conditions of parallelograms theorem if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram
conditions of parallelograms theorem if one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram
diagonals of a rectangle theorem if a paralleogram is a rectangle, then its diagonals are congruent
diagonals of a rectangle theorem if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
diagonals of a rhombus theorem if a parallelogram is a rhombus, then its diagonals are perpendicular
diagonals of a rhombus theorem if a parallelogram is a rhombus, then each diagonals bisects a pair of opposite angles
conditions for rhombi and squares theorem if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus
conditions for rhombi and squares theorem if one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus
conditions for rhombi and squares theorem if one pair of consecutive sides of a parallelogram are congruent, the parallelogram is a rhombus
conditions for rhombi and squares theorem if a quadrilateral is both a rectangle and a rhombus, then it is a square
isosceles trapezoids theorem if a trapezoid is isosceles, then each pair of base angles is congruent
isosceles trapezoids theorem if a trapezoid has one pair of congruent base angles, then it is an isosceles trapezoid
isoscleles trapezoids theorem a trapezoid is isosceles if and only if its diagonals are congruent
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
kites theorem if a quadrilateral is a kite, then its diagonals are perpendicular
kites theorem if a quadrilateral is a kite, then exactl yone pair of opposite angles is congruent

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