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Worksheet: Properties of Rhombi

Q1:

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.
  • AB and C
  • BA and B
  • CB and E
  • DB and D
  • ED and E

Q2:

If 𝐴 𝐡 𝐢 𝐷 is a rhombus, which line is the perpendicular bisector of 𝐴 𝐢 ?

  • A βƒ–      βƒ— 𝐴 𝐷
  • B βƒ–     βƒ— 𝐴 𝐡
  • C βƒ–     βƒ— 𝐢 𝐷
  • D βƒ–     βƒ— 𝐡 𝐷

Q3:

Are the opposite sides of a rhombus parallel?

  • A yes
  • B no

Q4:

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

  • Ayes
  • Bno

Q5:

Determine whether this statement is true or false: All rhombuses are regular polygons.

  • Afalse
  • Btrue

Q6:

Which of the following statements is NOT true for ALL rhombuses?

  • AIt has 2 pairs of angles equal in measure.
  • BIt is an equilateral polygon.
  • CIt has 2 pairs of parallel lines.
  • DIt is a parallelogram with 4 right angles.
  • EIt is a quadrilateral of sides equal in length.

Q7:

Given that is a rhombus with , what is ?

  • A
  • B
  • C
  • D

Q8:

Given that is a rhombus with , what is ?

  • A
  • B
  • C
  • D

Q9:

𝐴 𝐡 𝐢 𝐷 is a rhombus. If π‘š ∠ 𝐷 𝑃 𝐢 = ( 2 π‘₯ + 2 2 ) ∘ , find the value of π‘₯ .

Q10:

In a rhombus 𝐹 𝐺 𝐻 𝐽 , π‘š ∠ 𝐽 𝐹 𝐾 = ( 3 𝑦 + 6 ) ∘ and π‘š ∠ 𝐾 𝐹 𝐺 = ( 7 𝑦 βˆ’ 1 4 ) ∘ . Find the value of 𝑦 .

Q11:

Determine the measures of ∠ 𝑃 and ∠ 𝑄 in the rhombus 𝑂 𝑃 𝑄 𝑅 .

  • A π‘š ∠ 𝑃 = 5 3 ∘ , π‘š ∠ 𝑄 = 3 7 ∘
  • B π‘š ∠ 𝑃 = 7 4 ∘ , π‘š ∠ 𝑄 = 1 0 6 ∘
  • C π‘š ∠ 𝑃 = 3 7 ∘ , π‘š ∠ 𝑄 = 5 3 ∘
  • D π‘š ∠ 𝑃 = 1 0 6 ∘ , π‘š ∠ 𝑄 = 7 4 ∘

Q12:

In the given rhombus 𝐴 𝐡 𝐢 𝐷 , 𝐷 𝐡 = 6 π‘₯ βˆ’ 8 and 𝑃 𝐡 = 2 π‘₯ + 9 . Find the length of 𝑃 𝐷 .

Q13:

The figure shows rhombus 𝐴 𝐡 𝐢 𝐷 . Find π‘š ∠ 𝐡 𝐴 𝐢 and the length of 𝐴 𝐷 .

  • A 3 0 ∘ , 29 cm
  • B 6 0 ∘ , 14.5 cm
  • C 3 0 ∘ , 14.5 cm
  • D 6 0 ∘ , 29 cm

Q14:

In the given rhombus 𝐴 𝐡 𝐢 𝐷 , π‘š ∠ 𝐡 𝐢 𝐷 = 3 6 ∘ . Find π‘š ∠ 𝐡 𝐴 𝐢 .

Q15:

𝐴 𝐡 𝐢 𝐷 is a quadrilateral. The coordinates of the points 𝐴 , 𝐡 , and 𝐢 are ( 1 , 2 ) , ( βˆ’ 7 , 1 ) , and ( 0 , βˆ’ 3 ) respectively. Find the coordinates of point 𝐷 if the figure is a rhombus.

  • A ( 8 , βˆ’ 7 )
  • B ( 9 , βˆ’ 4 )
  • C ( 1 3 , 2 )
  • D ( 8 , βˆ’ 2 )

Q16:

Determine the perimeter of the rhombus 𝐴 𝐡 𝐢 𝐷 , given that the points 𝐴 and 𝐡 are ( βˆ’ 5 , βˆ’ 1 ) and ( βˆ’ 4 , 4 ) .

  • A26 length units
  • B √ 2 6 length units
  • C 2 √ 3 length units
  • D 4 √ 2 6 length units

Q17:

Given that the points 𝐴 ( βˆ’ 3 , 3 ) , 𝐡 ( 2 , βˆ’ 4 ) , 𝐢 ( 9 , βˆ’ 9 ) , and 𝐷 ( 4 , βˆ’ 2 ) are vertices of the rhombus 𝐴 𝐡 𝐢 𝐷 , find the coordinates of the point of intersection of its two diagonals.

  • A ( 0 , 0 )
  • B ( βˆ’ 6 , 6 )
  • C ( βˆ’ 3 , 3 )
  • D ( 3 , βˆ’ 3 )

Q18:

The figure shows a rhombus. Given that , what are the sizes of the angles at , , , and ?

  • A , , , and
  • B , , , and
  • C , , , and
  • D , , , and

Q19:

Is the following statement true or false? In a rhombus, all sides are equal in length.

  • Atrue
  • Bfalse

Q20:

Are the sides of a rhombus equal in length?

  • Ayes
  • Bno

Q21:

Are the two diagonals of a rhombus perpendicular?

  • Ayes
  • Bno

Q22:

Determine whether the following sentence is true or false: A rhombus has only one pair of parallel sides.

  • A false
  • B true

Q23:

In the rhombus shown, determine π‘š ∠ 𝑋 , π‘š ∠ π‘Œ , π‘š ∠ 𝑍 , and π‘š ∠ 𝐿 .

  • A 9 0 ∘ , 8 6 ∘ , 9 0 ∘ , 9 4 ∘
  • B 1 3 7 ∘ , 4 3 ∘ , 1 3 7 ∘ , 4 3 ∘
  • C 4 3 ∘ , 8 6 ∘ , 1 3 7 ∘ , 9 4 ∘
  • D 9 4 ∘ , 8 6 ∘ , 9 4 ∘ , 8 6 ∘

Q24:

Are the angles in a rhombus right angles?

  • Ano
  • Byes

Q25:

In which of these quadrilaterals are the diagonals perpendicular but not equal in length?

  • Asquare
  • Btrapezium
  • Crectangle
  • Drhombus