Worksheet: Properties of Rhombuses

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In this worksheet, we will practice identifying the properties of a rhombus and using them to find unknown angles or lengths.

Q1:

Given that 𝐴𝐵𝐶𝐷 is a rhombus with 𝑚∠𝐷𝐵𝐶=49∘, what is 𝑚∠𝐷𝐴𝐵?

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

Q2:

𝐴 𝐵 𝐶 𝐷 is a rhombus. If 𝑚∠𝐷𝑃𝐶=(2𝑥+22)∘, find the value of 𝑥.

Q3:

In a rhombus 𝐹𝐺𝐻𝐽, 𝑚∠𝐽𝐹𝐾=(3𝑦+6)∘ and 𝑚∠𝐾𝐹𝐺=(7𝑦−14)∘. Find the value of 𝑦.

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.
  • AD and E
  • BB and C
  • CB and D
  • DB and E
  • EA and B

Q5:

If 𝐴𝐵𝐶𝐷 is a rhombus, which line is the perpendicular bisector of 𝐴𝐶?

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

Q6:

Are the opposite sides of a rhombus parallel?

  • AYes
  • BNo

Q7:

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

  • Ano
  • Byes

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

Q10:

Determine the measures of ∠𝑃 and ∠𝑄 in the rhombus 𝑂𝑃𝑄𝑅.

  • A 𝑚 ∠ 𝑃 = 1 0 6 ∘ , 𝑚 ∠ 𝑄 = 7 4 ∘
  • B 𝑚 ∠ 𝑃 = 3 7 ∘ , 𝑚 ∠ 𝑄 = 5 3 ∘
  • C 𝑚 ∠ 𝑃 = 5 3 ∘ , 𝑚 ∠ 𝑄 = 3 7 ∘
  • D 𝑚 ∠ 𝑃 = 7 4 ∘ , 𝑚 ∠ 𝑄 = 1 0 6 ∘

Q11:

In the given rhombus 𝐴𝐵𝐶𝐷, 𝐷𝐵=6𝑥−8 and 𝑃𝐵=2𝑥+9. Find the length of 𝑃𝐷.

Q12:

The figure shows rhombus 𝐴𝐵𝐶𝐷. Find 𝑚∠𝐵𝐴𝐶 and the length of 𝐴𝐷.

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

Q13:

In the given rhombus 𝐴𝐵𝐶𝐷, 𝑚∠𝐵𝐶𝐷=36∘. Find 𝑚∠𝐵𝐴𝐶.

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

Q15:

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

  • A26 length units
  • B 4 √ 2 6 length units
  • C 2 √ 3 length units
  • D √ 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 𝐴𝐵𝐶𝐷, 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∠𝐴𝑀𝐻=50∘, what are the measures of the angles at 𝐴, 𝐵, 𝐶, and 𝐷?

  • A 4 0 ∘ , 5 0 ∘ , 4 0 ∘ , and 50∘
  • B 4 0 ∘ , 1 4 0 ∘ , 4 0 ∘ , and 140∘
  • C 8 0 ∘ , 1 0 0 ∘ , 8 0 ∘ , and 100∘
  • D 9 0 ∘ , 1 0 0 ∘ , 9 0 ∘ , and 80∘

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?

  • ANo
  • BYes

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.

  • Afalse
  • Btrue

Q22:

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

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

  • Atrapezium
  • Bsquare
  • Crhombus
  • Drectangle

Q25:

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

  • Adiagonals
  • Bsides

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