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


In geometry, a quadrilateral is a four-sided polygon with four angles. If you've ever seen a square or rectangle, you've seen a quadrilateral. Quadrilaterals are everywhere, and understanding them is an important part of learning geometry. Let's dive into the world of quadrilaterals and explore their different types, properties, and how they are used in real life.

What is a quadrilateral?

A quadrilateral is a figure that has four sides. These sides can be of different lengths, and the angles between the sides can also be different. Some characteristics of a quadrilateral are as follows:

  • He has four arms.
  • They have four corners.
  • They have four angles.

Quadrilaterals can be classified into different types depending on the lengths of the sides and the measures of the angles. Let's take a closer look at these.

ABCD

An example of a quadrilateral ABCD with four sides and four corners.

Types of quadrilaterals

1. Parallelogram

A parallelogram is a quadrilateral whose opposite sides are parallel. This means that each pair of opposite sides has the same length. Also, the opposite angles are equal. Here are some properties of a parallelogram:

  • Opposite sides are of equal length: AB = CD and AD = BC.
  • Opposite angles are equal: ∠A = ∠C and ∠B = ∠D.
  • The sum of the interior angles is 360 degrees.
  • The diagonals bisect each other.
ABCD

Representation of a parallelogram ABCD. AB ∥ CD and AD ∥ BC.

2. Rectangle

A rectangle is a parallelogram with four right angles. This means that each angle is 90 degrees. Some other properties of a rectangle are:

  • Opposite sides are equal and parallel: AB = CD and AD = BC.
  • Each angle is 90 degrees: ∠A = ∠B = ∠C = ∠D = 90°.
  • The length of the diagonals is equal.
ABCD

Illustration of a rectangle ABCD, showing that all angles are right angles.

3. Square

A square is a special type of quadrilateral in which all sides are of equal length and all angles are right angles. Therefore, a square is also a special type of rectangle. Its properties are as follows:

  • All sides are equal: AB = BC = CD = DA.
  • Each angle is 90 degrees.
  • The diagonals are equal in length and bisect each other at right angles.
ABCD

View of a square ABCD. All sides are equal in length, and every angle is a right angle.

4. Rhombus

A rhombus is a quadrilateral whose four sides are of equal length. However, unlike a square, the angles in a rhombus need not be 90 degrees. Here are its distinctive features:

  • All sides are equal: AB = BC = CD = DA.
  • Opposite angles are equal.
  • The diagonals bisect each other at right angles.
ABCD

A rhombus ABCD in which each side is of equal length.

5. Trapezium

A trapezoid, also called a trapezium, is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. Here are some characteristics:

  • At least one pair of opposite sides is parallel.
  • The angles between a leg and a base can be unequal.
ABCD

An example of a trapezoid ABCD, showing a pair of parallel sides AB and CD.

Properties of quadrilaterals

Understanding the properties of quadrilaterals is important in solving geometry problems. Here are some general properties that apply to all quadrilaterals:

  • The sum of all the interior angles of a quadrilateral is 360°.
  • Quadrilaterals can be either convex or concave. A convex quadrilateral has all interior angles less than 180°, while a concave quadrilateral has one angle greater than 180°.
  • Quadrilaterals can have multiple lines of symmetry depending on their specific type. For example, a square has four lines of symmetry, while a trapezoid may not have any lines of symmetry.

Calculating area and perimeter

Knowing how to calculate the area and perimeter of a quadrilateral is important in many practical applications, such as architecture and engineering.

Perimeter of a quadrilateral

The perimeter of a quadrilateral is the total length of the sides around it. It can be calculated by adding the lengths of all its sides.

Perimeter = AB + BC + CD + DA

Area of a quadrilateral

Calculating the area depends on the type of quadrilateral. Here is a simple formula for some special quadrilaterals:

Rectangle

Area = length × breadth

Social class

Area = side × side

Quadrilateral

Area = base × height

Quadrilateral

For a trapezoid, the area can be calculated by multiplying the average length of the parallel sides (bases) and the height:

Area = (base1 + base2) / 2 × height

Real life applications of quadrilaterals

Quadrilaterals can be found in many real-life situations. They are used in construction, design, and art, often forming the basis for complex structures. Rectangles and squares serve as basic units for tiling floors and walls. In graphic design, squares and rectangles are used as framing structures to create aesthetically pleasing graphics.

Conclusion

Quadrilaterals are fundamental shapes in geometry and form the basis of many calculations and designs. Whether you are measuring land, designing a building or simply creating a beautiful mosaic, understanding quadrilaterals is vital. By knowing the types and properties of quadrilaterals, you can gain a deeper understanding of shapes and their practical applications in everyday life.


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Quadrilaterals

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