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?

Q2:

𝐴𝐵𝐶𝐷 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?

  • A𝐶𝐷
  • B𝐴𝐷
  • C𝐵𝐷
  • D𝐴𝐵

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.

  • A𝑚𝑃=106, 𝑚𝑄=74
  • B𝑚𝑃=37, 𝑚𝑄=53
  • C𝑚𝑃=53, 𝑚𝑄=37
  • D𝑚𝑃=74, 𝑚𝑄=106

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.

  • A30, 29 cm
  • B60, 29 cm
  • C60, 14.5 cm
  • D30, 14.5 cm

Q13:

In the given rhombus 𝐴𝐵𝐶𝐷, 𝑚𝐵𝐶𝐷=36. Find 𝑚𝐵𝐴𝐶.

Q14:

𝐴𝐵𝐶𝐷 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(13,2)
  • 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
  • B426 length units
  • C23 length units
  • D26 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?

  • A40, 50, 40, and 50
  • B40, 140, 40, and 140
  • C80, 100, 80, and 100
  • D90, 100, 90, 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.

  • A43, 86, 137, 94
  • B137, 43, 137, 43
  • C90, 86, 90, 94
  • D94, 86, 94, 86

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?

  • Atrapezoid
  • Bsquare
  • Crhombus
  • Drectangle

Q25:

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

  • Adiagonals
  • Bsides

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