Explain how a square is (i) a quadrilateral
(ii) a parallelogram (iii) a rhombus (iv) a rectangle
Solution:
Steps:
| (i) | Quadrilateral | A square is a quadrilateral since it has four sides. |
| (ii) |
Parallelogram properties- (i) Opposite sides are equal. |
A square is a parallelogram since it contains both pairs of opposite sides which are equal, opposite angles are equal and its diagonals bisect each other. |
| (iii) |
Rhombus properties- i) A rhombus is a parallelogram with all sides of equal length. |
A square is a rhombus since i) All four sides are of the same length. |
| (iv) |
Rectangle properties- Being a parallelogram, the rectangle has opposite sides of equal length and its diagonals bisect each other and opposite angles are 90 degrees each. |
A square is a rectangle since each interior angle measures 90 degrees, opposite sides are of equal length and its diagonals bisect each other. |
☛ Check: NCERT Solutions for Class 8 Maths Chapter 3
Video Solution:
Explain how a square is. (i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle
NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.4 Question 3
Summary:
A square is (i) a quadrilateral as it has four sides. (ii) a parallelogram as it contains both pairs of opposite sides which are equal. (iii) a rhombus as its four sides are of the same length and the diagonals of a square are perpendicular bisectors of each other. (iv) a rectangle as each interior angle measures 90 degrees and opposite sides are of equal length and its diagonals bisect each other.
☛ Related Questions:
- Name the quadrilaterals whose diagonals. (i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal (i) parallelogram, rhombus, rectangle, and square bisect each other. (ii) square and rhombus are perpendicular bisectors of each other. (iii) rectangle and square are equal.
- Explain why a rectangle is a convex quadrilateral.
- ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).
- Identify all the quadrilaterals that have: (a) four sides of equal length (b) four right angles
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