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?

Q2:

𝐴𝐵𝐶𝐷 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?

  • A⃖⃗𝐶𝐷
  • B⃖⃗𝐴𝐷
  • C⃖⃗𝐵𝐷
  • D⃖⃗𝐴𝐵

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.

  • A𝑚∠𝑃=106∘, 𝑚∠𝑄=74∘
  • B𝑚∠𝑃=37∘, 𝑚∠𝑄=53∘
  • C𝑚∠𝑃=53∘, 𝑚∠𝑄=37∘
  • D𝑚∠𝑃=74∘, 𝑚∠𝑄=106∘

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.

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

Q13:

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

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
  • B4√26 length units
  • C2√3 length units
  • D√26 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?

  • 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 𝑚∠𝑋, 𝑚∠𝑌, 𝑚∠𝑍, and 𝑚∠𝐿.

  • 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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