Worksheet: Properties of Rectangles

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In this worksheet, we will practice solving problems using properties of rectangles.

Q1:

Does the measure of any angle in a rectangle equal 4 5 ∘ ?

  • ANo
  • BYes

Q2:

In rectangle 𝑋 𝑌 𝑍 𝐿 , which side length is equal to 𝑌 𝑍 ?

  • A 𝑌 𝐿
  • B 𝑋 𝑌
  • C 𝑋 𝐿

Q3:

In a rectangle 𝐴 𝐵 𝐶 𝐷 , which line is perpendicular to 𝐴 𝐵 ?

  • A 𝐷 𝐶
  • B 𝐴 𝐶
  • C 𝐴 𝐷

Q4:

Are the opposite angles equal in rectangles and parallelograms?

  • Ayes
  • Bno

Q5:

In the figure below, given that 𝐴 𝐵 𝐶 𝐷 is a rectangle, 𝑂 𝐵 𝐶 𝐻 is a parallelogram, and 𝐴 𝑂 = 3 . 7 c m , find the length of 𝐻 𝐴 .

Q6:

If 𝐹 𝐽 = 6 𝑥 + 8 𝑦 , 𝐹 𝑀 = 3 𝑥 + 5 𝑦 , 𝐺 𝐻 = 4 2 , and 𝐺 𝑀 = 2 4 , what values of 𝑥 and 𝑦 make parellelogram 𝐹 𝐺 𝐻 𝐽 a rectangle?

  • A 𝑥 = 3 , 𝑦 = 2 4
  • B 𝑥 = 4 2 , 𝑦 = 3
  • C 𝑥 = 4 2 , 𝑦 = 2 4
  • D 𝑥 = 3 , 𝑦 = 3
  • E 𝑥 = 4 2 , 𝑦 = 4 8

Q7:

Given that 𝐴 𝐵 𝐶 𝐷 is a rectangle, where 𝐸 𝐶 = 6 𝑥 − 7 and 𝐴 𝐸 = 2 𝑥 + 5 , find 𝐷 𝐸 .

Q8:

A rectangle is a special type of parallelogram that has .

  • Afour equal sides
  • Btwo perpendicular diagonals
  • Ca right angle

Q9:

Is the sum of two consecutive angles in rectangles and parallelograms equal to 1 8 0 ∘ ?

  • Ayes
  • Bno

Q10:

The two diagonals of a rectangle are .

  • Aperpendicular and equal in length
  • Bperpendicular
  • Cparallel
  • Dequal in length

Q11:

Are the angles in a rectangle right angles?

  • Ayes
  • Bno

Q12:

Which of the following statements must be true about a rectangle?

  • AIt has exactly one pair of parallel sides.
  • BIt has four sides of equal length.
  • CIt has four congruent sides.
  • DIt has two pairs of parallel opposite sides and four right angles.

Q13:

Do the sides of a rectangle have to be equal in length?

  • Ano
  • Byes

Q14:

What is the name for a parallelogram in which one of the angles is a right angle?

  • Aa rhombus
  • Ba trapezium
  • Ca rectangle

Q15:

Are the opposite sides of a rectangle parallel?

  • A Yes
  • B No

Q16:

Determine the diagonal length of the rectangle whose perimeter is 326.4 cm and length is 115.2 cm.

Q17:

A rectangular park has two walking paths as shown. If 𝑃 𝑆 = 1 0 0 m and 𝑃 𝑅 = 2 1 3 m , find the length of 𝑄 𝑇 .

Q18:

In this rectangle, 𝑋 𝑍 = 7 𝑐 , 𝑍 𝑌 = 2 1 , and 𝑋 𝑌 = 2 8 . Find the value of 𝑐 .

Q19:

Are the opposite angles in squares and rectangles equal?

  • Ayes
  • Bno

Q20:

In rectangle 𝑋 𝑌 𝑍 𝐿 , which side is perpendicular to 𝑌 𝑍 ?

  • A 𝑍 𝑋
  • B 𝑋 𝐿
  • C 𝑍 𝐿

Q21:

The diagonals of a rectangle are and .

  • Aequal in length, perpendicular
  • Bperpendicular, bisect each other
  • Cnot perpendicular, not equal in length
  • Dequal in length, bisect each other

Q22:

In a rectangle, all angles are angles.

  • Aacute
  • Bobtuse
  • Cright

Q23:

Are the diagonals of a rectangle always perpendicular?

  • Ano
  • Byes

Q24:

Do the two diagonals of a rectangle or a square bisect each other?

  • Ayes
  • Bno

Q25:

A square and a rectangle are .

  • Acongruent
  • Bsimilar
  • Cproportional
  • Dnot similar

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