How to Identify Adjacent Sides in Any Quadrilateral
A quadrilateral is a simple closed geometric figure with four sides and four angles. In simple words, a quadrilateral has four points lying in the same plane, out of which no three are collinear, and those points are joined by lines that do not intersect each other except at their common endpoints. A quadrilateral has 4 angles, 2 pairs of opposite sides and 4 pairs of adjacent sides each and a pair of diagonals.
Quadrilateral Examples:
Square, Rectangle, Kite, Rhombus, Parallelogram and Trapezium are examples of the quadrilateral.
A Rectangle
A Square
A Parallelogram
What are the Vertices of a Quadrilateral?
The common point joining the sides of a quadrilateral is said to be the vertices of a quadrilateral.
Quadrilateral
In quadrilateral ABCD, shown in the above figure, A, B, C and D are the vertices.
What are the edges of a quadrilateral?
The line segments joining the vertices of the quadrilateral are said to be the edges or sides of that quadrilateral.
In the quadrilateral ABCD shown above, AB, BC, AD and CD are the edges.
How many Diagonals does a Quadrilateral Have?
Let us see how many diagonals does quadrilateral have. The line segments joining the non-adjacent opposite vertices of a quadrilateral are called the diagonals of a quadrilateral. The diagonals of a quadrilateral intersect and bisect each other.
Number of Diagonals in Quadrilateral
In quadrilateral ABCD shown above, AC and BD are the diagonals.
How many Angles are there in a Quadrilateral?
Let us see how many angles does a quadrilateral have? Angles of a quadrilateral refer to the angles formed at each vertex by the adjacent sides of the quadrilateral. A quadrilateral has 4 angles. The sum of a quadrilateral's angles is \[360^\circ \].
In quadrilateral ABCD shown above, \[\angle {\rm{A}}\],\[\angle {\rm{B}}\],\[\angle {\rm{C}}\] and \[\angle {\rm{D}}\] are the angles of the quadrilateral.
Adjacent Sides of a quadrilateral
The sides of a quadrilateral with a common endpoint are called its adjacent sides.
Quadrilateral ABCD
In the given figure, (AB, BC), (BC, CD), (CD, DA) and (DA, AB) are four pairs of adjacent sides of quadrilateral ABCD.
Solved Examples :
Identify the pairs of adjacent sides from the given figure.
Solution: In the given quadrilateral, WXYZ, (WX, XY), (XY, YZ), (YZ, ZW) and (ZW, WX) are the pairs of adjacent sides.
Identify the pairs of adjacent sides from the given figure.
Solution: In the given quadrilateral PQRS, (PQ, QR), (QR, RS), (RS, SP) and (SP, PQ) are the pairs of adjacent sides.
Conclusion:
Thus, a quadrilateral is a closed figure with 4 vertices, 4 sides, 4 angles and 2 diagonals. A quadrilateral has 4 pairs of adjacent sides and 2 pairs of opposite sides. Talking about the angles, it has 2 pairs of opposite angles and 4 pairs of adjacent angles. Examples of quadrilaterals are Square, Rectangle, Rhombus, Parallelogram, Kite and Trapezium.
FAQs on Adjacent Sides of a Quadrilateral: Definition & Examples
1. What are the adjacent sides of a quadrilateral? Provide an example.
Adjacent sides of a quadrilateral are any two sides that share a common endpoint, known as a vertex. In any quadrilateral, there are four pairs of adjacent sides. For instance, in a quadrilateral named ABCD, the side AB and the side BC are adjacent because they both meet at the vertex B. The other pairs of adjacent sides are (BC, CD), (CD, DA), and (DA, AB).
2. How are adjacent sides different from opposite sides in a quadrilateral?
The key difference lies in their connection point. Adjacent sides meet at a common vertex, while opposite sides do not share any vertex and are directly across from each other. In quadrilateral PQRS:
- (PQ, QR) is a pair of adjacent sides as they meet at vertex Q.
- (PQ, RS) is a pair of opposite sides as they do not share any common point.
3. Which types of quadrilaterals are defined by having equal adjacent sides?
Two main types of quadrilaterals are specifically defined by their adjacent sides being equal:
- Kite: A kite has two distinct pairs of equal-length adjacent sides. For example, if AB = AD and CB = CD, the figure is a kite.
- Rhombus: A rhombus has all four sides equal in length. This means that every pair of adjacent sides is equal.
4. What are adjacent angles in a quadrilateral, and how do they relate to adjacent sides?
Adjacent angles are two angles in a quadrilateral that share a common side (or arm). The relationship is direct: two adjacent sides create the vertex where an interior angle is formed. For example, in quadrilateral ABCD, the adjacent sides AD and AB form the vertex A, which contains ∠DAB. The angles ∠A and ∠B are adjacent angles because they share the common side AB.
5. If a quadrilateral is labelled PQRS, how many pairs of adjacent sides can be identified?
For any quadrilateral, including one labelled PQRS, there are always four pairs of adjacent sides. These pairs are formed by the sides that meet at each of the four vertices:
- PQ and QR (meeting at vertex Q)
- QR and RS (meeting at vertex R)
- RS and SP (meeting at vertex S)
- SP and PQ (meeting at vertex P)
6. Is there a rule that the lengths of adjacent sides of a quadrilateral must add up to 180?
No, this is a common misconception. The lengths of sides are a measure of distance and do not have a relationship that requires them to sum to 180. The value 180 degrees relates to angles. In some specific quadrilaterals, like a parallelogram or a trapezoid, a pair of adjacent angles (not sides) can be supplementary, meaning they add up to 180°.
7. How is the concept of adjacent sides applied in real-world examples?
The concept of adjacent sides is fundamental in construction, architecture, and design. For example:
- In construction, when building a rectangular room, it is crucial that the adjacent walls (representing adjacent sides) meet at a perfect 90-degree angle.
- In design and engineering, the frame of a traditional kite relies on the properties of its adjacent sides to ensure aerodynamic stability.
- In land surveying, properties are often mapped as quadrilaterals, and the lengths of adjacent sides are measured to define the plot's boundary.
8. Why can't a quadrilateral have four obtuse angles?
This is impossible because it violates the Angle Sum Property of Quadrilaterals. An obtuse angle measures more than 90°. If a quadrilateral had four obtuse angles, the sum of its interior angles would be greater than 4 × 90° = 360°. However, the sum of the interior angles of any convex quadrilateral must be exactly 360°. Therefore, a quadrilateral cannot have all four angles as obtuse.
9. Are squares and rectangles considered quadrilaterals with adjacent sides?
Yes, absolutely. A square and a rectangle are special types of quadrilaterals. They satisfy the fundamental definition of a quadrilateral, which is a closed polygon with four sides, four vertices, and four angles. They also have four pairs of adjacent sides, just like any other quadrilateral. Their special properties, such as having all right angles, simply make them more specific classifications within the quadrilateral family.
