Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Geometry → Quadrilaterals ↓


Types of Quadrilaterals


In geometry, a quadrilateral is a four-sided polygon. Quadrilaterals come in many different shapes and variations, each with their own unique properties. Understanding these different types can help us understand the variety of geometric shapes and solve problems involving these shapes. This comprehensive guide will explore the types of quadrilaterals in detail and provide plenty of examples to illustrate each type. Let's start with the basics.

Definition of quadrilateral

A quadrilateral is any closed shape with four sides and four vertices. The word "quadrilateral" comes from the Latin words "quadri" meaning four, and "latus" meaning side. Quadrilaterals can be simple, with sides that do not intersect, or they can be complex, with sides that do intersect.

Basic properties of quadrilaterals

  • A quadrilateral has four sides.
  • It has four angles.
  • The sum of the interior angles of a quadrilateral is always 360 degrees.
Sum of angles = 360°

Types of quadrilaterals

Quadrilaterals can be divided into several different categories based on their properties. We will explore the following types:

  1. Quadrilateral
  2. Rectangle
  3. Rhombus
  4. Social class
  5. Trapezoid (or trapezoid)
  6. Kite
  7. Irregular quadrilateral

1. Parallelogram

A parallelogram is a quadrilateral in which the opposite sides are parallel. This results in the opposite sides being equal in length and the opposite angles being equal.

A B C D
  • Opposite sides are parallel: AB || CD and AD || BC.
  • Opposite sides are equal: AB = CD and AD = BC.
  • Opposite angles are equal: ∠A = ∠C and ∠B = ∠D.

Examples of parallelograms include rhombuses, rectangles, and squares.

2. Rectangle

A rectangle is a special type of parallelogram where all the angles are right angles (90 degrees). This means that opposite sides are equal and every angle is 90 degrees.

A B C D
  • All angles are 90 degrees: ∠A = ∠B = ∠C = ∠D = 90°.
  • Opposite sides are equal: AB = CD and AD = BC.

Rectangles are found everywhere in real life, from books to computer screens.

3. Rhombus

The rhombus is another type of parallelogram. It has four equal sides, but unlike the square, the angles are not necessarily 90 degrees.

A B C D
  • All sides are equal: AB = BC = CD = DA.
  • Opposite angles are equal: ∠A = ∠C and ∠B = ∠D.

Note that a rhombus with a right angle is actually a square.

4. Square

A square is a special type of both a rectangle and a rhombus. It has all the properties of these shapes plus additional symmetry.

A B C D
  • All sides are equal: AB = BC = CD = DA.
  • All angles are equal: ∠A = ∠B = ∠C = ∠D = 90°.

The use of squares is common in many tiling patterns and design layouts.

5. Trapezoid (or trapezoid)

A trapezoid is a quadrilateral with only one pair of parallel sides. In North America it is called a trapezium and elsewhere a trapezium.

A B C D
  • One pair of sides is parallel: AB || CD.

This shape is often seen in bridges, such as suspension bridges, where the cables form a trapezoidal shape.

6. Kite

A kite is a quadrilateral with two adjacent sides equal. Its shape resembles a flying kite.

A B C D
  • Two pairs of equal adjacent sides: AB = AD and BC = CD.
  • The diagonals are perpendicular.

Kites are often seen in decorative patterns and yes, even kite flying!

7. Irregular quadrilateral

An irregular quadrilateral is a shape that has no special properties with respect to sides, angles or symmetry. In such a quadrilateral, all sides and angles can be different. It does not fall into any of the other specific types mentioned above.

A B C D

These quadrilaterals can appear in a variety of freeform designs and are not bound by the rules of parallelism, symmetry, or angle measurement.

Conclusion

Quadrilaterals are versatile shapes that are used in a variety of mathematical contexts. Their properties are essential for solving geometric problems, such as finding area and perimeter or understanding how shapes interact in space. Knowing the different types of quadrilaterals and their properties can be of great help in practical applications, engineering, architecture, and more.

With this understanding of quadrilaterals, including parallelograms, rectangles, rhombuses, squares, trapezoids, rhombuses and irregular quadrilaterals, you are now well equipped to identify and analyse these quadrilateral shapes in your studies and beyond!


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Types of Quadrilaterals

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