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Worksheet: Properties of Squares and Their Applications

Q1:

Are the two diagonals of a square perpendicular?

  • Ayes
  • Bno

Q2:

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

  • Ayes
  • Bno

Q3:

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

  • Aa triangle
  • Ba rectangle
  • Ca square

Q4:

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

  • AIt has four sides of equal length.
  • BIt has two pairs of parallel opposite sides.
  • CIt has four right angles.
  • DAll these statements are true.

Q5:

𝐴 𝐡 𝐢 𝐷 is a square. What is the ratio of the lengths 𝐢 𝑀 : 𝐡 𝑀 ?

  • A 1 : 3
  • B 1 : 4
  • C 1 : 2
  • D 1 : 1

Q6:

𝐴 𝐡 𝐢 𝐷 is a square. What is the ratio of the lengths 𝐴 𝑀 : 𝑀 𝐡 ?

  • A 1 : 3
  • B 1 : 4
  • C 1 : 2
  • D 1 : 1

Q7:

In the square of the figure, 𝐴 𝐡 is 160 cm long, what is the length of 𝑀 𝐢 ?

Q8:

In the square of the figure, 𝐴 𝐡 is 304 cm long, what is the length of 𝑀 𝐢 ?

Q9:

Find the perimeter of the square below, and determine if .

  • A 240 cm,
  • B 120 cm,
  • C 120 cm,
  • D 240 cm,

Q10:

Given that 𝐴 𝐡 𝐢 𝐷 is a square, find, in degrees, the values of π‘₯ and 𝑦 .

  • A π‘₯ = 3 5 ∘ , 𝑦 = 1 4 5 ∘
  • B π‘₯ = 1 2 5 ∘ , 𝑦 = 3 5 ∘
  • C π‘₯ = 4 5 ∘ , 𝑦 = 1 2 5 ∘
  • D π‘₯ = 3 5 ∘ , 𝑦 = 1 2 5 ∘

Q11:

Given that 𝐴 𝐡 𝐢 𝐷 is a square, find, in degrees, the values of π‘₯ and 𝑦 .

  • A π‘₯ = 2 5 ∘ , 𝑦 = 1 5 5 ∘
  • B π‘₯ = 1 1 5 ∘ , 𝑦 = 2 5 ∘
  • C π‘₯ = 4 5 ∘ , 𝑦 = 1 1 5 ∘
  • D π‘₯ = 2 5 ∘ , 𝑦 = 1 1 5 ∘

Q12:

In the square the points are collinear. Given that , find .

  • A
  • B
  • C
  • D

Q13:

In the square the points are collinear. Given that , find .

  • A
  • B
  • C
  • D

Q14:

Given that is a square and , find .

  • A
  • B
  • C
  • D

Q15:

Given that 𝐴 𝐡 𝐢 𝐷 is a square whose perimeter is 232 cm, find the lengths of 𝐴 𝐡 and 𝐢 𝐸 . Then find area of β–³ 𝐸 𝐷 𝐡 .

  • A 𝐴 𝐡 = 5 8 c m , 𝐢 𝐸 = 2 9 c m , area of β–³ 𝐸 𝐷 𝐡 = 1 6 8 2 c m 2
  • B 𝐴 𝐡 = 1 5 . 2 3 c m , 𝐢 𝐸 = 7 . 6 2 c m , area of β–³ 𝐸 𝐷 𝐡 = 5 8 . 0 3 c m 2
  • C 𝐴 𝐡 = 1 5 . 2 3 c m , 𝐢 𝐸 = 7 . 6 2 c m , area of β–³ 𝐸 𝐷 𝐡 = 1 1 6 . 0 5 c m 2
  • D 𝐴 𝐡 = 5 8 c m , 𝐢 𝐸 = 2 9 c m , area of β–³ 𝐸 𝐷 𝐡 = 8 4 1 c m 2
  • E 𝐴 𝐡 = 1 5 . 2 3 c m , 𝐢 𝐸 = 7 . 6 2 c m , area of β–³ 𝐸 𝐷 𝐡 = 2 3 2 . 1 1 c m 2

Q16:

Is the following statement true or false? In a square, all angles are right angles and all sides are equal in length.

  • Atrue
  • Bfalse

Q17:

What is the size of any angle in a square?

  • A
  • B
  • C
  • D

Q18:

In which of the following shapes are all the sides the same length?

  • Atrapezoid
  • Brectangle
  • Cparallelogram
  • Dsquare

Q19:

Does a square have right angles?

  • Ayes
  • Bno

Q20:

𝐴 𝐡 𝐢 𝐷 is a square. What is the ratio of the lengths 𝐷 𝑀 : 𝑀 𝐡 ?

  • A 1 : 3
  • B 1 : 4
  • C 1 : 2
  • D 1 : 1

Q21:

Are the opposite sides of a square parallel?

  • A yes
  • B no

Q22:

Are any of the angles in a square 4 5 ∘ ?

  • A no
  • B yes

Q23:

All squares .

  • Aare not similar
  • Bare congruent
  • Chave the same area
  • Dare similar