Rectangle Rhombus Theorems

The diagram below shows parallelogram ABCD with diagonals AC and BD intersecting at E. What additional information is sufficient to prove that parallelogram ABCD is also a rhombus?

• AB is parallel to CD

• AC is congruent to BD

• BD bisects AC

• AC is perpendicular to BD

The diagram below shows parallelogram ABCD with diagonals AC and BD intersecting at E. What additional information is sufficient to prove that parallelogram ABCD is also a rectangle?

• AC is perpendicular to BD

• AC bisects BD

• AC is congruent to BD

• AC and BD bisect their respective angles

A parallelogram is a rectangle if

• Adjacent sides are perpendicular

• Diagonals are perpendicular

• Opposite sides are congruent

• Opposite angles are congruent

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

A parallelogram is a rhombus if

• Adjacent sides are congruent

• Diagonals bisect each other

• Opposite sides are congruent

• Adjacent sides are perpendicular

Figure A is a...

• Rectangle

• Square

• Rhombus

In a rhombus, opposite angles are __________.

• congruent

• supplementary

• corresponding

• parallel

Which of the following are NOT true about diagonals of a rhombus?

• they are perpendicular

• they bisect each other

• they are congruent

The figure is a rhombus.  
Solve for x.  

• 1

• 11

• 7

• 6

Name the following shape: 

• Rhombus

• Rectangle

• Square