Worksheet: Properties of Rhombuses

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 𝑚𝐷𝐵𝐶=49, what is 𝑚𝐷𝐴𝐵?

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

Q2:

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

Q3:

In a rhombus 𝐹𝐺𝐻𝐽, 𝑚𝐽𝐹𝐾=(3𝑦+6) and 𝑚𝐾𝐹𝐺=(7𝑦14). 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=6𝑥8 and 𝑃𝐵=2𝑥+9. Find the length of 𝑃𝐷.

Q12:

The figure shows rhombus 𝐴𝐵𝐶𝐷. Find 𝑚𝐵𝐴𝐶 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, 𝑚𝐵𝐶𝐷=36. Find 𝑚𝐵𝐴𝐶.

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 𝑚𝐴𝑀𝐻=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 𝑚𝑋, 𝑚𝑌, 𝑚𝑍, and 𝑚𝐿.

  • 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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