What are the Types and Properties of Quadrilaterals?
The concept of understanding quadrilaterals class 8 is a key part of geometry in the Class 8 Maths curriculum. It helps students identify and differentiate between four-sided figures, study their properties, and solve exam-focused questions quickly and accurately.
What Is Understanding Quadrilaterals?
A quadrilateral is a polygon with four sides, four angles, and four vertices. Understanding quadrilaterals means knowing how to classify various four-sided polygons (such as rectangles, squares, parallelograms, rhombuses, trapeziums, and kites), learning the characteristics of each, and applying formulas for angle calculations, area, and perimeter. You’ll find this concept applied in geometry, mensuration, and even in real-world problems involving shapes and measurements.
Key Formulas for Quadrilaterals
Here are the standard formulas every Class 8 student should remember:
- Angle Sum Property: The sum of all interior angles in any quadrilateral is 360°.
- Perimeter: Add the lengths of all four sides.
- Area: Varies by type:
Rectangle: \( \text{Area} = \text{Length} \times \text{Breadth} \)
Square: \( \text{Area} = \text{Side}^2 \)
Parallelogram: \( \text{Area} = \text{Base} \times \text{Height} \)
Trapezium: \( \text{Area} = \frac{1}{2} \times (\text{Sum of Parallel Sides}) \times \text{Height} \)
Kite/Rhombus: \( \text{Area} = \frac{1}{2} \times \text{Product of Diagonals} \)
Types of Quadrilaterals in Class 8 Maths
| Type | Key Properties | Example |
|---|---|---|
| Rectangle | Opposite sides equal and parallel; all angles are 90°; diagonals equal and bisect each other. | Book, Wall |
| Square | All sides equal; all angles 90°; diagonals equal and bisect at 90°. | Chessboard, Window Pane |
| Parallelogram | Opposite sides equal and parallel; opposite angles equal; diagonals bisect each other. | Slanted Tabletop |
| Rhombus | All sides equal; opposite angles equal; diagonals bisect at right angles. | Diamond, Kite Shape |
| Trapezium | Only one pair of parallel sides. | Bridge, Notebook Stand |
| Kite | Two pairs of adjacent sides equal; one diagonal bisected; one pair of opposite angles equal. | Actual Kite |
| Irregular Quadrilateral | No specific equal sides or parallel sides/angles; any four-sided figure. | Plot Boundary |
Properties of Important Quadrilaterals (Quick Reference Table)
| Property | Rectangle | Square | Parallelogram | Rhombus | Trapezium |
|---|---|---|---|---|---|
| Sides | Opp. equal | All equal | Opp. equal | All equal | 1 pair parallel |
| Angles | All 90° | All 90° | Opp. equal | Opp. equal | Any |
| Diagonals Equal | Yes | Yes | No | No | No |
| Diagonals Bisect Angles | No | Yes | No | Yes | No |
How to Solve Quadrilaterals Questions: Step-by-Step Example
Example: In a quadrilateral, three angles measure 90°, 110°, and 85°. Find the fourth angle.
1. List the given angles: 90°, 110°, and 85°2. Recall the angle sum property: All angles add up to 360°
3. Add the given angles: 90 + 110 + 85 = 285°
4. Subtract from 360° to find the missing angle: 360 − 285 = 75°
Final Answer: The missing angle is 75°.
Speed Trick or Vedic Shortcut
When solving quadrilateral questions in exams:
- If you know three angles, simply subtract their total from 360° to get the fourth.
- For rectangles and squares, remember: Diagonals are always equal.
- In parallelograms, adjacent angles add to 180°.
Practicing these mental shortcuts helps you save precious time in MCQs and written tests. Vedantu’s online classes cover many such tricks and tips with stepwise examples.
Try These Yourself
- Draw a parallelogram and mark all equal sides and angles.
- List the differences between a rectangle and a square in your own words.
- If a trapezium has parallel sides 8 cm and 4 cm, height 5 cm, find its area.
- Identify which of these is NOT a quadrilateral: triangle, rhombus, kite, square.
Frequent Errors and Misunderstandings
- Confusing parallelogram, rhombus, and rectangle properties.
- Forgetting that the sum of all quadrilateral angles is always 360° (not 180° or 720°).
- Mixing up which quadrilaterals have equal diagonals.
- Assuming all quadrilaterals have both pairs of sides parallel (only parallelograms do).
Relation to Other Concepts
The topic of understanding quadrilaterals connects closely to types of quadrilaterals, the angle sum property of quadrilateral, and general concepts of polygons in geometry. It’s also foundational for understanding area and perimeter, as well as for solving problems on area and perimeter of various shapes.
Classroom Tip
A simple way to remember the sum of angles in any quadrilateral is: draw a four-sided figure and split it into two triangles from one vertex. Each triangle has 180°, so 2 × 180 = 360°. Vedantu teachers often demonstrate this with diagrams for better concept clarity.
We explored understanding quadrilaterals class 8—from definition, types, formulas, differences, solved examples, and key mistakes. Keep practicing with Vedantu to master properties and problem-solving in quadrilaterals!
Explore More: Types of Quadrilaterals | Practice Worksheets |
FAQs on Understanding Quadrilaterals – Class 8 Maths
1. What is a quadrilateral in Maths for class 8?
A quadrilateral is a closed two-dimensional geometric shape with four sides, four angles, and four vertices. Understanding quadrilaterals involves learning about their different types, properties, and how to calculate their area and perimeter.
2. How many types of quadrilaterals are there?
There are several types of quadrilaterals, each with its own unique properties. Common types include: parallelograms (including rectangles, squares, and rhombuses), trapeziums, and kites. There are also irregular quadrilaterals.
3. What are the properties of a parallelogram?
A parallelogram has the following properties:
- Opposite sides are parallel and equal in length.
- Opposite angles are equal.
- Adjacent angles are supplementary (add up to 180°).
- Diagonals bisect each other.
4. Why is the sum of angles in a quadrilateral always 360°?
The sum of interior angles in any quadrilateral is always 360°. This can be proven by dividing the quadrilateral into two triangles. Each triangle has angles that add up to 180°, and since there are two triangles, the total sum is 180° + 180° = 360°.
5. How to quickly identify a square vs. rectangle in a question?
A square is a special type of rectangle. Both have four right angles (90°). However, a square has all four sides equal in length, while a rectangle only has opposite sides equal.
6. Where can I find understanding quadrilaterals class 8 worksheets with answers?
Vedantu provides numerous resources, including worksheets and solved examples, to help you understand quadrilaterals. Check our website for practice materials aligned with the Class 8 syllabus.
7. What is the difference between a rhombus and a parallelogram?
A rhombus is a type of parallelogram. All parallelograms have opposite sides parallel and equal, but a rhombus has the additional property that *all* its sides are equal in length.
8. What is the importance of diagonals in classifying quadrilaterals?
Diagonals play a crucial role in identifying different types of quadrilaterals. For example, the properties of diagonals (whether they bisect each other, are equal in length, or are perpendicular) help distinguish between parallelograms, rhombuses, rectangles, and squares.
9. How do real-world paths, plots, or windows relate to quadrilateral concepts?
Many everyday objects and structures exhibit quadrilateral shapes. For instance, building foundations, window panes, picture frames, and even some traffic signs are often based on quadrilateral geometries like rectangles and squares.
10. How to calculate the area of a trapezium?
The area of a trapezium is calculated using the formula: Area = ½ × (sum of parallel sides) × height. Remember that the 'height' is the perpendicular distance between the parallel sides.
11. What are the properties of a kite?
A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. Its diagonals are perpendicular to each other, and one diagonal bisects the other.
12. What are some common mistakes students make when dealing with quadrilaterals?
Common mistakes include confusing the properties of different quadrilaterals (e.g., mixing up the properties of rectangles and rhombuses), incorrectly identifying parallel sides, and making errors in calculating areas and perimeters due to incorrect formula application or unit conversions.
