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 → Practical Geometry → Construction of Quadrilaterals ↓


Quadrilaterals Given Side Lengths and Angles


Quadrilaterals are four-sided polygons that can take various shapes. In practical geometry, especially at the grade 7 level, constructing quadrilaterals when given side lengths and angles is a basic skill. These constructions help students understand geometric principles in a practical way. In this section, we will take a closer look at how to construct quadrilaterals when given specific side lengths and angles.

Understanding quadrilaterals

A quadrilateral is simply a polygon with four edges (or sides) and four vertices (or corners). Common types of quadrilaterals include squares, rectangles, trapezoids, rhombuses, and parallelograms. But there are countless other possible quadrilaterals if we don’t limit ourselves to these categories.

Basic properties

  • A quadrilateral has four sides, four angles and the sum of its interior angles is always 360°.
  • Depending on the angles and side lengths, the shape and properties of a quadrilateral can vary widely.

Construction with given side lengths and angles

When drawing a quadrilateral where the lengths of some sides and angles are given, there are certain steps that must be followed. Usually, you will be given the lengths of all four sides and the measurement of at least one angle. Let’s explore this through detailed examples and visual representations.

Step-by-step construction guide

Example 1: Construction of quadrilateral ABCD

Suppose you are provided with the following information:

  • AB = 5 cm
  • BC = 4 cm
  • CD = 6 cm
  • DA = 7 cm
  • Angle A = 90°

Follow these steps to construct this quadrilateral:

Step 1: Make the base

Start by drawing the base AB. Use the ruler to draw a straight line segment AB equal to 5 cm.

Step 2: Construct angle A

Using the protractor, construct an angle A = 90° at point A. This will help you align the side AD.

Step 3: Draw the line AD

Draw a line AD measuring 7 cm from point A using a ruler, forming a right angle.

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Step 4: Complete the quadrilateral

To complete the quadrilateral, follow these additional steps:

  • Using the length of BC (4 cm), measure and mark point C from point B.
  • Join points C and D using the remaining side, making sure the length of CD is 6 cm.
Now Advertisement BC CD D A B C

Verification of construction

Double-check the length of each side using a ruler and make sure the angles are measured correctly with the protractor. The sum of all angles should be 360°.

Examples with other given angles

Example 2: Two given angles

Sometimes, instead of providing one angle, two angles can be provided along with the length of the sides. For example, let us consider:

  • AB = 5 cm, BC = 4 cm, CD = 6 cm, DA = 7 cm
  • Angle A = 60°, Angle B = 120°

In this case, the process begins in a similar way, but will require careful planning around the given angles. Draw AB, then use the protractor to mark the angle A = 60°. Measure and mark AD = 7 cm. From A, adjust the protractor to help identify the direction of DA. Next, use the protractor at point B to mark the angle B = 120° and proceed accordingly.

Visual representation

Now Advertisement DC BC A B D C

Completion of construction

Finally, adjust and measure from C to D, making sure that CD = 6 cm. Verify the opposite angles and sides to accurately complete the quadrilateral. Always verify that the sum of the angle measures is 360°.

Practice problems

To get good at constructing quadrilaterals with given side lengths and angles, practice with different dimensions:

Problem 1

  • AB = 8 cm, BC = 6 cm, CD = 5 cm, DA = 7 cm
  • Angle A = 90°

Problem 2

  • AB = 10 cm, BC = 8 cm, CD = 6 cm, DA = 9 cm
  • Angle A = 85°, Angle C = 100°

Solve these problems step by step, as in the examples above, and verify your quadrilateral construction using a ruler and protractor.

Conclusion

Constructing quadrilaterals given their side lengths and angles is a crucial component of understanding geometry at a foundational level. Using clear step-by-step procedures, proper use of tools like rulers and protractors, and constant practice, anyone can master this aspect of practical geometry. Remember, performing each step correctly ensures that the quadrilateral will be accurate and reflect the given measurements and angles.


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Construction of Quadrilaterals
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Quadrilaterals Given Side Lengths and Angles

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