Download Special Parallelograms

Special Parallelograms
Geometry, ch. 6
NAME:
Fill each blank with always, sometimes, or never:
Squares are always
rhombuses.
Rhombuses are sometimes
squares.
Squares are always
rectangles.
Rhombuses are sometimes
rectangles.
Squares are always
parallelograms.
Rhombuses are always
parallelograms.
Squares are never
trapezoids.
Rhombuses are never
trapezoids.
Squares are always
quadrilaterals.
Rhombuses are always
quadrilaterals.
Rectangles are sometimes
rhombuses.
Parallelograms are sometimes
squares.
Rectangles are sometimes
squares.
Parallelograms are sometimes
rhombuses.
Rectangles are always
parallelograms.
Parallelograms are sometimes
rectangles.
Rectangles are never
trapezoids.
Parallelograms are never
trapezoids.
Rectangles are always
quadrilaterals.
Parallelograms are always
quadrilaterals.
Trapezoids are never
squares.
Quadrilaterals are sometimes
squares.
Trapezoids are never
rhombuses.
Quadrilaterals are sometimes
rhombuses.
Trapezoids are never
rectangles.
Quadrilaterals are sometimes
rectangles.
Trapezoids are never
parallelograms.
Quadrilaterals are sometimes
parallelograms.
Trapezoids are always
quadrilaterals.
Quadrilaterals are sometimes
trapezoids.
Decide whether each statement is true or false:
_____ 1. All rhombuses are squares. (F)
_____ 7. If a parallelogram is a rectangle, then it is also a rhombus. (F)
_____ 2. No trapezoids are parallelograms. (T)
_____ 8. If a quadrilateral is a parallelogram, then it is also a rhombus.
(F)
_____ 3. Some rectangles are rhombuses. (T)
_____ 4. Some parallelograms are quadrilaterals. (F)
_____ 5. All squares are parallelograms. (F)
_____ 6. If a parallelogram is a square, then it is also a rectangle. (T)
_____ 9.
If a quadrilateral is a rhombus, then it is also a parallelogram.
(T)
_____ 10.
If a quadrilateral is a trapezoid, then it can’t be a
parallelogram. (T)
For each shape, identify whether the property is always true (A), sometimes true (S), or never true (N):
SQUARES:
RHOMBUSES:
A Both pairs of opposite sides are parallel.
A Both pairs of opposite sides are parallel.
A Both pairs of opposite sides are equal.
A Both pairs of opposite sides are equal.
A All four sides are equal.
A All four sides are equal.
A Opposite pairs of angles are equal.
A Opposite pairs of angles are equal.
A All four angles are equal.
S
A The diagonals bisect each other.
A The diagonals bisect each other.
A The diagonals bisect the corner angles.
A The diagonals bisect the corner angles.
A The diagonals are congruent.
S
A The diagonals are perpendicular.
A The diagonals are perpendicular.
RECTANGLES:
A Both pairs of opposite sides are parallel.
All four angles are equal.
The diagonals are congruent.
PARALLELOGRAMS:
A Both pairs of opposite sides are parallel.
A Both pairs of opposite sides are equal.
A Both pairs of opposite sides are equal.
S
S
All four sides are equal.
All four sides are equal.
A Opposite pairs of angles are equal.
A Opposite pairs of angles are equal.
A All four angles are equal.
S
A The diagonals bisect each other.
A The diagonals bisect each other.
S
S
The diagonals bisect the corner angles.
A The diagonals are congruent.
S
The diagonals are congruent.
S
S
The diagonals are perpendicular.
The diagonals bisect the corner angles.
The diagonals are perpendicular.
Decide whether each statement is true or false:
_____ 11.
If a quadrilateral is a parallelogram, then the diagonals are congruent. (F)
_____ 12.
If a parallelogram is a rectangle, then the diagonals bisect each other. (F)
_____ 13.
If a parallelogram is a square, then the diagonals bisect the corner angles. (T)
_____ 14.
If a quadrilateral is a rhombus, then all four angles are equal. (F)
All four angles are equal.