A quadrilateral whose four sides and angles are equal to each other is known as
Square
Understanding Quadrilaterals with Equal Sides and Angles
A quadrilateral is a four-sided polygon. The question asks us to identify a specific type of quadrilateral that possesses two key properties simultaneously: its four sides are equal in length, and its four angles are equal in measure.
Analyzing the Properties of Different Quadrilaterals
Let's examine the characteristics of the quadrilaterals listed in the options to see which one fits the description:
- Square: A Square is defined as a quadrilateral with four sides of equal length and four right angles. Since all right angles measure \(90^\circ\), they are equal to each other. Therefore, a Square has four equal sides and four equal angles.
- Rectangle: A rectangle is a quadrilateral with four right angles. Its opposite sides are equal in length, but its adjacent sides are not necessarily equal. So, while it has four equal angles, it does not necessarily have four equal sides.
- Rhombus: A rhombus is a quadrilateral with four sides of equal length. Its opposite angles are equal, but its adjacent angles are not necessarily equal (unless it's also a rectangle). So, while it has four equal sides, it does not necessarily have four equal angles.
- Parallelogram: A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Its opposite angles are also equal. However, its sides are not necessarily all equal, and its angles are not necessarily all equal (adjacent angles are supplementary).
Comparing Quadrilateral Properties
We can summarize the properties related to sides and angles in the following table:
| Quadrilateral Type | Four Equal Sides? | Four Equal Angles? | Fits Description? |
|---|---|---|---|
| Square | Yes | Yes (\(90^\circ\) each) | Yes |
| Rectangle | No (only opposite sides) | Yes (\(90^\circ\) each) | No |
| Rhombus | Yes | No (only opposite angles) | No |
| Parallelogram | No (only opposite sides) | No (only opposite angles, adjacent are supplementary) | No |
Conclusion: Identifying the Correct Quadrilateral
Based on the analysis of the properties, only the Square satisfies both conditions mentioned in the question: having four sides equal to each other and four angles equal to each other. A Square is essentially a rhombus that is also a rectangle.
Therefore, a quadrilateral whose four sides and angles are equal to each other is known as a Square. Understanding the geometry properties of shapes like quadrilaterals helps in classifying them correctly based on their sides and angles.
Important Questions from Quadrilaterals
The ratio between the length and breadth of a rectangular park is 3 : 2. If a man cycling along the boundary at the speed of 12 km per hour completes one round in 8 minutes, then the area of the park in square meter will be
The sides of a quadrilateral are in the ratio of 3 ∶ 4 ∶ 6 ∶ 8. If the perimeter of the quadrilateral is 84 cm. Find the longest side of the quadrilateral.
The side of a rhombus is 26 cm. The length of one of its diagonals is 20 cm. The sum of the lengths of the diagonals of this rhombus is equal to the perimeter of a rectangle. If the difference between the length and breadth of the rectangle is 6 cm, then what is the area of the rectangle?
PQRS is a cyclic quadrilateral. If ∠P is 4 times ∠R, and ∠S is 3 times ∠Q, then the average of ∠Q and ∠R is:
ABCD is a trapezium in which AB || DC and DC is perpendicular to BC. If ∠DAB = 110°, then ∠ABC - ∠ADC =_____.
