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


In practical geometry, learning to draw quadrilaterals is an essential part of understanding how shapes can be drawn and measured accurately. A quadrilateral is a polygon with four sides and four vertices. The four sides, four angles, and the sum of the interior angles, which is always 360 degrees, are important properties of quadrilaterals.

Basic concepts and terminology

  • Vertex: The point where two sides of a polygon meet.
  • Sides: The line segments that make up the polygon.
  • Diagonal: A line segment connecting two disjoint vertices within a polygon.
  • Interior angles: Angles formed inside the polygon.

The different types of quadrilaterals include squares, rectangles, parallelograms, rhombuses, kites, and trapezoids. Each has unique properties that affect the way they are constructed.

Types of quadrilaterals

Social class

A square is a quadrilateral whose four sides are of equal length and all angles are equal to 90 degrees.

Rectangle

A rectangle is a quadrilateral in which opposite sides are equal and each angle is 90 degrees.

Quadrilateral

The opposite sides of a parallelogram are equal and parallel, and the opposite angles are also equal.

Rhombus

A rhombus is a parallelogram with all sides of equal length.

Kite

A kite has two pairs of adjacent sides that are equal in length.

Quadrilateral

A trapezoid has a pair of opposite sides that are parallel.

Stages of construction of a quadrilateral

When constructing a quadrilateral the following data must be known:

  • Four sides and one diagonal
  • Three sides and two diagonals
  • Two adjacent sides and three angles
  • Three sides and two included angles

Step-by-step construction of a quadrilateral using four sides and a diagonal

Let us take an example of constructing a quadrilateral ABCD, given four sides AB, BC, CD, DA and diagonal AC:

  1. Draw line AB = 6 cm.
  2. From point A draw an arc of radius equal to AC.
  3. From point B draw an arc of radius equal to BC which cuts the previous arc at C.
  4. Join AC and BC.
  5. From point C draw an arc of radius equal to CD.
  6. Draw an arc of radius equal to DA from point A which cuts the arc drawn from C at D.
  7. Join CD and DA. Quadrilateral ABCD is constructed.
Given: AB = 6 cm, BC = 5 cm, CD = 4 cm, DA = 5 cm, AC = 7 cm

∙ A──B (6cm)
   
∙ ____C (5cm)
 /
∙ D (4cm)
Shape: Quadrilateral ABCD

Step-by-step construction of a quadrilateral using three sides and two diagonals

Consider the construction of quadrilateral PQRS, given three sides PQ, QR, RS, and diagonals PR and QS:

  1. Draw line PQ = 5 cm.
  2. Draw an arc of radius PR = 8 cm from point P.
  3. From point Q, draw an arc of radius QR = 7 cm which cuts the first arc at R.
  4. Join PR and QR.
  5. Draw an arc of radius RS = 6 cm from point R.
  6. From point P draw an arc QS = 9 cm which cuts the arc drawn from R at S.
  7. Join RS and PS to complete the quadrilateral PQRS.
Given: PQ = 5 cm, QR = 7 cm, RS = 6 cm, PR = 8 cm, QS = 9 cm

∙ P──Q (5cm)
   
∙ ____R (7cm)
 /
∙ S (6cm)
Figure: Quadrilateral PQRS

Step-by-step construction of a quadrilateral using two adjacent sides and three angles

Construct the quadrilateral EFGH given two adjacent sides EF, FG, and three angles <EFG, <FGH, and <GHE:

  1. Draw line EF = 4 cm.
  2. At point F draw angle <EFG = 60 degrees and make FG = 5 cm.
  3. Construct angle <FGH = 90 degrees at point G.
  4. Using a compass, take a radius equal to GH and draw an arc.
  5. Similarly, angle <GHE = 120 degrees and draw an arc at point H.
  6. Intersect the arcs drawn from G and H to find point E.
  7. Join HE to complete the quadrilateral EFGH.
Given: EF = 4 cm, FG = 5 cm
Angles: <EFG = 60°, <FGH = 90°, <GHE = 120°

∙ E──F (4 cm)
  
∙  g (5cm)
∙ ∕ / (60°)
∙ H (90°)
Figure: Quadrilateral EFGH

Step-by-step construction with three sides and two included angles

Consider the construction of a quadrilateral IJKL, given three sides IJ, JK, KL, and two angles <IJK and <JKL:

  1. Draw line IJ = 7 cm.
  2. At point J, construct an angle <IJK = 75 degrees and draw JK = 6 cm.
  3. Draw an arc at point K making angle <JKL = 120 degrees.
  4. Take radius KL = 5 cm from K and intersect it with the arc drawn from L to get point L.
  5. Add IL as needed to complete the quadrilateral.
Given: IJ = 7 cm, JK = 6 cm, KL = 5 cm
Angles: <IJK = 75°, <JKL = 120°

∙ I──J (7cm)
  
∙ ____k (6 cm)
∙ ∕ / (75°)
∙ L (120°)
Figure: Quadrilateral IJKL

Properties of diagonal in quadrilateral

To construct quadrilaterals it is important to understand the properties of diagonals:

  • Diagonals of a parallelogram: They bisect each other.
  • Diagonals of a rectangle: They are equal in length and bisect each other.
  • Diagonals of a rhombus: They bisect each other at right angles.
  • Diagonals of a square: They are equal and bisect each other at right angles.

These properties can guide you to accurately construct quadrilaterals from given measurements.

Conclusion

Understanding basic geometric concepts and properties is essential to construct quadrilaterals accurately. By practicing different methods of constructing quadrilaterals with given sides, angles, and diagonals, students can develop a strong foundation in practical geometry. This knowledge is not only important in mathematics, but it also applies to real-world applications such as engineering and design.


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Constructing Right-Angled Triangles
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Quadrilaterals Given Side Lengths and Angles

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Construction of Quadrilaterals

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