Worksheet: Properties of Rhombuses

In this worksheet, we will practice identifying a rhombus and learning about its properties.

Q1:

Given that 𝐴 𝐵 𝐶 𝐷 is a rhombus with 𝑚 𝐷 𝐵 𝐶 = 4 9 , what is 𝑚 𝐷 𝐴 𝐵 ?

  • A 1 3 1
  • B 4 9
  • C 7 7
  • D 8 2

Q2:

is a rhombus. If , find the value of .

  • A11
  • B79
  • C56
  • D34
  • E4

Q3:

In a rhombus , and . Find the value of .

  • A13
  • B9
  • C8
  • D5
  • E18

Q4:

Choose from the following statements the properties of a rhombus.

  1. It has four right angles.
  2. It has two pairs of angles equal in measure.
  3. It has only one pair of parallel sides.
  4. It is a parallelogram of four sides of equal length.
  5. It is a parallelogram of four equal angles.
  • AB and C
  • BA and B
  • CB and E
  • DB and D
  • ED and E

Q5:

If 𝐴 𝐵 𝐶 𝐷 is a rhombus, which line is the perpendicular bisector of 𝐴 𝐶 ?

  • A 𝐴 𝐷
  • B 𝐴 𝐵
  • C 𝐶 𝐷
  • D 𝐵 𝐷

Q6:

Are the opposite sides of a rhombus parallel?

  • A Yes
  • B No

Q7:

Do the two diagonals of a rectangle and a rhombus bisect each other?

  • Ayes
  • Bno

Q8:

Determine whether this statement is true or false: All rhombuses are regular polygons.

  • Afalse
  • Btrue

Q9:

Which of the following statements is NOT true for ALL rhombuses?

  • AIt has 2 pairs of angles equal in measure.
  • BIt is an equilateral polygon.
  • CIt has 2 pairs of parallel lines.
  • DIt is a parallelogram with 4 right angles.
  • EIt is a quadrilateral of sides equal in length.

Q10:

Determine the sizes of and in the rhombus .

  • A ,
  • B ,
  • C ,
  • D ,

Q11:

In the given rhombus 𝐴 𝐵 𝐶 𝐷 , 𝐷 𝐵 = 6 𝑥 8 and 𝑃 𝐵 = 2 𝑥 + 9 . Find the length of 𝑃 𝐷 .

Q12:

The figure shows rhombus 𝐴 𝐵 𝐶 𝐷 . Find 𝑚 𝐵 𝐴 𝐶 and the length of 𝐴 𝐷 .

  • A 3 0 , 29 cm
  • B 6 0 , 14.5 cm
  • C 3 0 , 14.5 cm
  • D 6 0 , 29 cm

Q13:

In the given rhombus , . Find .

  • A
  • B
  • C
  • D
  • E

Q14:

𝐴 𝐵 𝐶 𝐷 is a quadrilateral. The coordinates of the points 𝐴 , 𝐵 , and 𝐶 are ( 1 , 2 ) , ( 7 , 1 ) , and ( 0 , 3 ) respectively. Find the coordinates of point 𝐷 if the figure is a rhombus.

  • A ( 8 , 7 )
  • B ( 9 , 4 )
  • C ( 1 3 , 2 )
  • D ( 8 , 2 )

Q15:

Determine the perimeter of the rhombus 𝐴 𝐵 𝐶 𝐷 , given that the points 𝐴 and 𝐵 are ( 5 , 1 ) and ( 4 , 4 ) .

  • A26 length units
  • B 2 6 length units
  • C 2 3 length units
  • D 4 2 6 length units

Q16:

Given that the points 𝐴 ( 3 , 3 ) , 𝐵 ( 2 , 4 ) , 𝐶 ( 9 , 9 ) , and 𝐷 ( 4 , 2 ) are vertices of the rhombus 𝐴 𝐵 𝐶 𝐷 , find the coordinates of the point of intersection of its two diagonals.

  • A ( 0 , 0 )
  • B ( 6 , 6 )
  • C ( 3 , 3 )
  • D ( 3 , 3 )

Q17:

The figure shows a rhombus. Given that 𝑚 𝐴 𝑀 𝐻 = 5 0 , what are the measures of the angles at 𝐴 , 𝐵 , 𝐶 , and 𝐷 ?

  • A 9 0 , 1 0 0 , 9 0 , and 8 0
  • B 4 0 , 5 0 , 4 0 , and 5 0
  • C 4 0 , 1 4 0 , 4 0 , and 1 4 0
  • D 8 0 , 1 0 0 , 8 0 , and 1 0 0

Q18:

Is the following statement true or false? In a rhombus, all sides are equal in length.

  • Atrue
  • Bfalse

Q19:

Are the sides of a rhombus equal in length?

  • Ayes
  • Bno

Q20:

Are the two diagonals of a rhombus perpendicular?

  • AYes
  • BNo

Q21:

Determine whether the following sentence is true or false: A rhombus has only one pair of parallel sides.

  • A false
  • B true

Q22:

In the rhombus shown, determine 𝑚 𝑋 , 𝑚 𝑌 , 𝑚 𝑍 , and 𝑚 𝐿 .

  • A 9 0 , 8 6 , 9 0 , 9 4
  • B 1 3 7 , 4 3 , 1 3 7 , 4 3
  • C 4 3 , 8 6 , 1 3 7 , 9 4
  • D 9 4 , 8 6 , 9 4 , 8 6

Q23:

Are the angles in a rhombus right angles?

  • ANo
  • BYes

Q24:

In which of these quadrilaterals are the diagonals perpendicular but not equal in length?

  • Asquare
  • Btrapezium
  • Crectangle
  • Drhombus

Q25:

A rhombus is a square if its are equal in length.

  • Adiagonals
  • Bsides

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