Lesson Worksheet: Properties of Rhombuses Mathematics • 11th Grade

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:

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

Q3:

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

  • A𝐶𝐷
  • B𝐴𝐷
  • C𝐵𝐷
  • D𝐴𝐵

Q4:

Are the opposite sides of a rhombus parallel?

  • AYes
  • BNo

Q5:

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

  • ANo
  • BYes

Q6:

True or False: All rhombuses are regular polygons.

  • AFalse
  • BTrue

Q7:

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.

Q8:

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

Q9:

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

Q10:

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

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