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Lesson: Properties of Squares and Their Applications

In this lesson, we will learn how to solve problems using properties of squares.

Sample Question Videos

04:28

Worksheet • 23 Questions • 1 Video

Q1:

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

  • Aa rectangle
  • Ba square
  • Ca triangle

Q2:

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

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

Q3:

Given that 𝐴 𝐡 𝐢 𝐷 is a square and π‘š ∠ 𝐸 𝐷 𝐢 = 6 2 ∘ , find π‘š ∠ 𝐷 𝐸 𝐴 .

Q4:

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 = 8 4 1 c m 
  • B 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 
  • C 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 
  • D 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 
  • E 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 

Q5:

Are the two diagonals of a square perpendicular?

  • Ano
  • Byes

Q6:

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

  • Ano
  • Byes

Q7:

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

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

Q8:

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

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

Q9:

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

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

Q10:

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

Q11:

Find the perimeter of the square 𝐴 𝐡 𝐢 𝐷 below, and determine π‘š ∠ 𝐸 𝐢 𝐷 if π‘š ∠ 𝐡 𝐢 𝐸 = 7 0 ∘ .

  • A 240 cm, 2 0 ∘
  • B 120 cm, 7 0 ∘
  • C 120 cm, 4 5 ∘
  • D 240 cm, 9 0 ∘

Q12:

In the square 𝐴 𝐡 𝐢 𝐷 the points 𝐡 , 𝐢 , 𝑂 a n d are collinear. Given that π‘š ∠ 𝑂 𝐴 𝐢 = 2 8 ∘ , find π‘š ∠ 𝐴 𝑂 𝐢 .

Q13:

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

  • Afalse
  • Btrue

Q14:

What is the measure of any angle in a square?

Q15:

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

  • Asquare
  • Brectangle
  • Cparallelogram
  • Dtrapezium

Q16:

Does a square have right angles?

  • Ano
  • Byes

Q17:

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

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

Q18:

Are the opposite sides of a square parallel?

  • A no
  • B yes

Q19:

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

  • A yes
  • B no

Q20:

All squares .

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

Q21:

Are the sides of a square equal in length?

  • Ano
  • Byes

Q22:

What can you say about the diagonals of a square?

  • AThey are perpendicular and equal in length.
  • BThey are just perpendicular.
  • CThey are neither perpendicular nor equal in length.
  • DThey are just equal in length.

Q23:

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

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