Proving Rectangle, Rhombus, and Square

A parallelogram must be a rhombus if its diagonals

• are congruent

• bisect each other

• do not bisect its angles

• are perpendicular to each other

A parallelogram is always a rectangle if

• the diagonals are congruent

• the diagonals bisect each other

• the diagonals intersect at right angles

• the opposite angles are congruent

Which information is not sufficient to prove that a parallelogram is a square?

• The diagonals are both congruent and perpendicular.

• The diagonals are congruent and one pair of adjacent sides are congruent.

• The diagonals are perpendicular and one pair of adjacent sides are congruent.

• The diagonals are perpendicular and one pair of adjacent sides are perpendicular.

Which of the following group of quadrilaterals have diagonals that are perpendicular to each other?

I. Parallelogram

II. Rectangle

III. Rhombus

IV. Square

• All of the above

• II, III and IV

• II and IV, only

• III and IV, only

Which of the following group of quadrilaterals have congruent diagonals?

I. Parallelogram

II. Rectangle

III. Rhombus

IV. Square

• All of the above

• II, III and IV

• II and IV, only

• III and IV, only

Which information is sufficient to prove that a parallelogram is a square?

• The diagonals are perpendicular and one pair of adjacent sides are congruent.

• The diagonals are congruent and the adjacent sides are perpendicular.

• The diagonals bisect each other and one pair of adjacent sides are perpendicular.

• The diagonals are both congruent and perpendicular.

A parallelogram is a square if it has all the properties of

• a rhombus and rectangle

• a parallelogram and rhombus

• a parallelogram and rectangle

• trapezoid and rhombus

Which property is shown in the parallelogram that makes it a rectangle?

• Diagonals are perpendicular

• Adjacent sides are perpendicular

• Diagonals bisect each other

• Opposite angles are congruent

Which property is shown in the parallelogram that makes it a rectangle?

• Diagonals are perpendicular to each other

• Diagonals bisect each other

• opposite sides congruent

• Diagonals are congruent to each other

Which property is shown in the parallelogram that makes it a rhombus?

• Opposite sides are congruent

• Diagonals are perpendicular to each other

• Adjacent sides are congruent

• Diagonals are congruent