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definition of a parallelogram a quadrilateral with both pairs of opposite sides parallel
five properties/theorems for parallelograms opposite sides are parallel, diagonals bisect each other, opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary
definition of a rectangle a quadrilateral with four right angles
rectangle theorems if a parallelogram is a rectangle, then its diagonals are congruent; if the diagonals of a parallelogram are congruent, then the paralellogram is a rectangle
five properties of a rectangle opposite sides are congruent and parallel; opposite angles are congruent; consecutive angles are supplementary; diagonals are congruent and bisect each other; all four angles are right angles
definition of a rhombus a quadrilateral with four congruent sides
rhombus theroems the diagonals of a rhombus are perpendicular; if the diagonals of a parallelogram are perpendicular, then the paralellogram is a rhombus; each diagonal of a rhombus bisects a pair of opposite angles
properties of a rhombus all parallelogram properties apply; all four sides are congruent; diagonals are perpendicular; the diagonals bisect opposite angles
definition of a square a quadrilateral with four right angles and four congruent sides
properties of a square the properties of a rectangle plus the properties of a rhombus; four right angles; all four sides are congruent
definition of a trapezoid a quadrilateral with exactly one pair of parallel sides
definition of an isosceles trapezoid a trapezoid with the legs congruent
isosceles trapezoid theroems both pairs of base angles are congruent; the diagonals are congruent
trapezoid median theorem the median of a trapezoid is parallel to the bases and its measure is one-half the sum of the measures of the bases, or median=1/2(x+y)
in these quadrilaterals, the diagonals bisect each other paralellogram, rectangle, rhombus, square
in these quadrilaterals, the diagonals are congruent rectangle, square, isosceles trapezoid
in these quadrilaterals, each of the diagonals bisects a pair of opposite angles rhombus, square
in these quadrilaterals, the diagonals are perpendicular rhombus, square
a rhombus is always a... parallelogram
a square is always a... parallelogram, rhombus, and rectangle
a rectangle is always a... parallelogram
a square is never a... trapezoid, because trapezoids only have one pair of parallel sides
a trapezoid is never a... parallelogram, rhombus, rectangle, or square, because trapezoids only have one pair of parallel sides
these quadrilaterals always have all four congruent sides rhombus, square
these quadrilaterals always have all four right angles rectangle, square
these quadrilaterals always have perpendicular diagonals rhombus, square
if you divide a square into four right triangles by drawing its two diagonals, the measure of each of the angles in the triangles that is not a right angle is... 45 degrees
the diagonals of a rhombus... are not always congruent, but they are always perpendicular and they do always bisect each other, and they do always bisect the pairs of opposite angles
the diagonals of a rectangle... are not always perpendicular, but they are always congruent and they always bisect each other
the diagonals of a parallelogram... always bisect each other