| A | B |
|---|
| 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 |
