What is Square?
Square is a plane figure or a quadrilateral with four equal sides and angles. All the four angles of the square are at right angles. The two opposite sides of a square are always of equal length.
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Properties of a Square
- The four interior angles of a square are equal to 90°.
- Four sides of a square are congruent and equal to each other.
- Opposite sides of a square are equal and parallel to each other.
- The two diagonals of a square are equal and bisect each other at 90°.
- The area of a square is equal to side× side.
- The two equal diagonals of a square make two similar isosceles triangles.
What is a Rhombus?
Rhombus is also known as diamond or rhombus diamond is a parallelogram and a four- sided quadrilateral. In Rhombus, opposite angles and sides are equal in length and parallel. The diagonals of a square bisect each other at 90°. Rhombi or Rhombuses is a plural form of a rhombus.
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Properties of a Rhombus
- Sides of a rhombus are equal
- Opposite sides of a rhombus are parallel.
- Diagonals bisect each other at 90° in rhombus
- No circumscribing and inscribing circles can be made around rhombus.
- A diagonal of a rhombus bisects its angles.
- Two adjacent angles of a rhombus are equal to 180°.
Rhombus and Square Differences and Similarities
The Below Table Shows Some Points on Rhombus and Square Differences.
The Below Table Shows Some Points on Similarities Between Rhombus and Square.
Is a Square a Rhombus?
Square is a rhombus because as rhombus all the sides of a square are equal in length. Even, the diagonals of both square and rhombus are perpendicular to each other and bisect the opposite angles. Therefore, we can say the square is a rhombus.
The table drawn above which shows similarities between rhombus and square proves the sentence “Is a square a rhombus”?
1. Calculate the area of a rhombus having diagonals equal to 12 cm and 8 cm.
Solution- Given that,
Diagonal 1 or d₁ =12 cm
Diagonal 2 or d₂ = 8 cm
Area of a rhombus = (d₁ x d₂)
= (12 x 8)/ 2
= 43 cm²
2. Let all the area of the square equal to 8 cm. Find its area, perimeter and length of diagonal.
Solution -Side of a square =8 cm
Area of a square = s²= 8² = 64 cm²
Perimeter of a square = 4 x a= 4 x 8 cm=32 cm
Length of the diagonal of a square = s√2 = 1.414 x 8 =11.312
- The word rhombus is derived from the Greek word rhombus, which means ‘Spinning top’.
- Sometimes rhombus are called as diamond, but not all rhombi are diamond in shape
- The sum of the four internal angles of a square is 360°.
- Square which means ‘honest’ or fair is initially recorded in the 1560s
Which of the following statements is true about rhombus?
a. All the sides of a rhombus are congruent
b. The diagonals of a rhombus are congruent
c. Rhombus has 4 right angles
d. All of the above
Which of the following statements are true about the square?
a. The diagonals of a square are congruent
b. The sides of a square are congruent
c. The square has four right angles
d. The diagonals of a square are perpendicular