Prove Rhombus

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

A parallelogram must be a rhombus if its diagonals

• are congruent

• bisect each other

• do not bisect its angles

• are perpendicular to each other

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

• Diagonals are perpendicular to each other

• Diagonals are congruent to each other

• Diagonals are bsiect each other

• Adjacent sides are perpendicular

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

• Diagonals are perpendicular to each other

• Diagonals bisect each other

• Diagonals bisect their respective angles

• Diagonals are congruent

To prove that the following parallelogram PQRS is a rhombus, which of the following must be true?

• PQ⊥PS

• PR≅SQ

• ∠8≅∠1 and ∠4≅∠5

• ∠3≅∠12 and ∠2≅∠11

Match the missing statements & reasons in the proof.

f

b

d

e

a

c

g

Reflexive

ABCD is Parallelogram

Rhombus 4 = sides

ABCD Rhombus

CPCTC

Opp sides Parallel in Parallelogram

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

In order to show that a figure is a rhombus, you first need to prove it is a ...

• Quadrilateral

• Square

• Rectangle

• Parallelogram

Brad proved that ABCD is a parallelogram by proving both sets of opposite sides to be parallel. What should he do next if he wants to prove it is a rhombus?

• Find the distance of each line to see if they are congruent. 

• Compare the slopes of adjacent sides to see if they are perpendicular. 

Sarah proved that each side has a distance of \sqrt{29} . What does this mean?

• All 4 sides are congruent

• All 4 sides form right angles

• All opposite sides are parallel