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 𝐴𝐡𝐢𝐷 is a rhombus with π‘šβˆ π·π΅πΆ=49∘, what is π‘šβˆ π·π΄π΅?

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 𝐴𝐡𝐢𝐷 is a rhombus, which line is the perpendicular bisector of 𝐴𝐢?

  • A⃖⃗𝐢𝐷
  • B⃖⃗𝐴𝐷
  • C⃖⃗𝐡𝐷
  • D⃖⃗𝐴𝐡

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 βˆ π‘ƒ and βˆ π‘„ in the rhombus 𝑂𝑃𝑄𝑅.

  • Aπ‘šβˆ π‘ƒ=106∘, π‘šβˆ π‘„=74∘
  • Bπ‘šβˆ π‘ƒ=37∘, π‘šβˆ π‘„=53∘
  • Cπ‘šβˆ π‘ƒ=53∘, π‘šβˆ π‘„=37∘
  • Dπ‘šβˆ π‘ƒ=74∘, π‘šβˆ π‘„=106∘

Q9:

The figure shows rhombus 𝐴𝐡𝐢𝐷. Find π‘šβˆ π΅π΄πΆ and the length of 𝐴𝐷.

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

Q10:

In the given rhombus 𝐴𝐡𝐢𝐷, π‘šβˆ π΅πΆπ·=36∘. Find π‘šβˆ π΅π΄πΆ.

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