Class 8 Practical Geometry: Notes, Steps & Solved Questions

Practical Geometry Class 8 – Introduction

Practical Geometry is an important chapter in Class 8 Maths that teaches students how to construct different geometrical figures accurately using a ruler, compass and protractor. In this chapter, students learn how to construct quadrilaterals when some of their sides, angles, diagonals or other measurements are given. The main idea is to use the given information carefully and follow a proper sequence of construction steps.

Quick Answer: In Class 8 Practical Geometry, the most important skill is to construct a quadrilateral from given measurements. Before starting a construction, identify the given sides, angles and diagonals, draw the fixed part first, and then locate the remaining vertices using arcs and angle measurements.

What is Practical Geometry?

Practical Geometry deals with the actual construction of geometrical figures. Unlike ordinary geometry questions where we mainly calculate lengths or angles, practical geometry requires us to draw a figure accurately according to the given conditions.

For example, if the lengths of four sides and one diagonal of a quadrilateral are given, we can construct the quadrilateral by first drawing the diagonal and then locating the other vertices with the help of a compass.

Important Instruments Used

• Ruler: Used to draw line segments and measure lengths.
• Compass: Used to draw arcs and transfer lengths.
• Protractor: Used to measure and construct angles.
• Pencil: Used for accurate and neat construction.
• Eraser: Used to remove unnecessary construction lines after completion.

Important Note: In construction questions, accuracy is more important than making the diagram large. Keep the pencil sharp and use the ruler and compass carefully.

Types of Quadrilateral Constructions

In Class 8 Practical Geometry, we mainly learn how to construct a quadrilateral when different combinations of measurements are given. The construction can be possible when enough information is provided to determine the quadrilateral uniquely.

Common types of information given in questions include:

• Four sides and one diagonal
• Two diagonals and three sides
• Two adjacent sides and three angles
• Three sides and two included angles
• Some sides and angles along with a diagonal

Basic Construction Principles

Before solving a construction problem, remember that a quadrilateral has four sides and four vertices. The information given in the question must be used in a logical order.

Basic Idea: Draw the known line segment first → construct the given angle or length → locate the unknown point using arcs → join the required vertices → verify the construction.

Why is a Diagonal Useful?

A quadrilateral can be divided into two triangles by drawing one diagonal. Since triangles are easier to construct, a diagonal often becomes the starting point for constructing a quadrilateral.

For example, quadrilateral ABCD can be divided into triangles ABC and ACD by diagonal AC.

Quadrilateral ABCD + Diagonal AC = Triangle ABC + Triangle ACD

This idea is extremely useful in construction problems because once the diagonal is drawn, the remaining points can often be located by constructing triangles.

Construction Using Four Sides and One Diagonal

Suppose the four sides of quadrilateral ABCD and diagonal AC are given. We can construct it by first drawing AC and then constructing two triangles on either side of AC.

Steps of Construction

1. Draw the given diagonal AC using a ruler.
2. With A as centre and radius equal to AB, draw an arc.
3. With C as centre and radius equal to BC, draw another arc cutting the first arc at B.
4. Join AB and BC.
5. Now, with A as centre and radius equal to AD, draw an arc on the other side of AC.
6. With C as centre and radius equal to CD, draw another arc cutting the previous arc at D.
7. Join AD and CD.
8. The required quadrilateral ABCD is obtained.

Remember: When four sides and one diagonal are given, the diagonal divides the quadrilateral into two triangles. Construct one triangle on one side of the diagonal and the second triangle on the other side.

Construction When Two Diagonals and Three Sides are Given

Sometimes a question gives the lengths of two diagonals and three sides. In such cases, use one diagonal as the base and construct the remaining vertices using the given lengths.

General Method

1. Draw one of the given diagonals.
2. Use the given side lengths to locate one vertex with arcs.
3. Use the second diagonal length to locate the opposite vertex.
4. Join all the required vertices.
5. Check whether the remaining given side agrees with the construction.

Exam Tip: Always read the construction question completely before drawing anything. Decide which given measurement can be used as the starting line segment.

Construction Using Two Adjacent Sides and Three Angles

Suppose two adjacent sides and three angles of a quadrilateral are given. We can construct the quadrilateral by first drawing one known side, constructing an angle at one endpoint, marking the second side, and then constructing the remaining angles.

Step-by-Step Method

1. Draw one of the given sides using a ruler.
2. At one endpoint, construct the given angle using a protractor.
3. On the constructed ray, mark the second given side.
4. At the new vertex, construct the next given angle.
5. Continue the construction using the remaining angle information.
6. Join the final point to complete the quadrilateral.

Construction Using Three Sides and Two Included Angles

When three sides and two included angles are given, the construction is usually started with one of the known sides.

1. Draw the first given side.
2. Construct the first given angle at one endpoint.
3. Mark the second side on the constructed ray.
4. Construct the second given angle at the appropriate vertex.
5. Mark the third given side.
6. Join the remaining vertices to complete the quadrilateral.

Key Rule: A construction is successful only when the given measurements determine the figure sufficiently and all required conditions can be satisfied.

Important Properties Used in Practical Geometry

Although this chapter focuses on construction, several basic geometry properties are useful while solving questions.

• A quadrilateral has 4 sides and 4 vertices.
• The sum of the interior angles of a quadrilateral is 360°.
• A diagonal divides a quadrilateral into two triangles.
• A triangle can be constructed using suitable combinations of sides and angles.
• Equal lengths can be transferred accurately using a compass.
• Angles can be copied or constructed using a protractor.

Sum of angles of a quadrilateral = 360°

15 Important Practical Geometry Questions with Solutions

Question 1: What instruments are required for practical geometry constructions?

Solution:

The main instruments required are a ruler, compass and protractor. A sharp pencil and eraser are also useful for neat construction.

The ruler is used for line segments, the compass is used for arcs and transferring lengths, and the protractor is used for measuring and constructing angles.

Question 2: How many sides does a quadrilateral have?

Solution:

A quadrilateral has 4 sides, 4 vertices and 4 angles.

The word "quadrilateral" means a polygon with four sides.

Question 3: What is the sum of the interior angles of a quadrilateral?

Solution:

Draw one diagonal in a quadrilateral. It divides the quadrilateral into two triangles.

Each triangle has an angle sum of 180°.

180° + 180° = 360°

Therefore, the sum of the interior angles of a quadrilateral is 360°.

Question 4: Construct a quadrilateral ABCD when AB = 4 cm, BC = 5 cm, CD = 4 cm, DA = 5 cm and AC = 6 cm.

Solution:

1. Draw AC = 6 cm.
2. With A as centre and radius 4 cm, draw an arc.
3. With C as centre and radius 5 cm, draw another arc cutting the first at B.
4. Join AB and BC.
5. With A as centre and radius 5 cm, draw an arc on the opposite side of AC.
6. With C as centre and radius 4 cm, draw another arc cutting it at D.
7. Join AD and CD.
8. ABCD is the required quadrilateral.

Question 5: Why is a diagonal helpful in constructing a quadrilateral?

Solution:

A diagonal divides a quadrilateral into two triangles. Since triangles are easier to construct using known sides and angles, constructing the diagonal makes the quadrilateral construction simpler.

Question 6: Construct a quadrilateral when four sides are 5 cm, 4 cm, 6 cm and 5 cm and one diagonal is 7 cm.

Solution:

1. Draw the diagonal of 7 cm.
2. Using the first two side lengths as radii, draw arcs from the two endpoints of the diagonal.
3. The intersection gives the first unknown vertex.
4. Using the other two side lengths, draw arcs on the opposite side.
5. The second intersection gives the other unknown vertex.
6. Join all vertices.

The required quadrilateral is obtained.

Question 7: What is the role of a compass in construction?

Solution:

A compass is used to draw arcs and transfer lengths accurately. It helps us locate points that are at a fixed distance from a given point.

Question 8: Construct a quadrilateral ABCD when AB = 5 cm, BC = 4 cm, CD = 6 cm, DA = 5 cm and diagonal AC = 7 cm.

Solution:

1. Draw AC = 7 cm.
2. From A, draw an arc of radius 5 cm.
3. From C, draw an arc of radius 4 cm.
4. Their intersection gives B.
5. From A, draw an arc of radius 5 cm on the other side.
6. From C, draw an arc of radius 6 cm.
7. The intersection gives D.
8. Join AB, BC, CD and DA.

Question 9: If three angles of a quadrilateral are 80°, 100° and 90°, find the fourth angle.

Solution:

Sum of angles = 360°

Fourth angle = 360° − (80° + 100° + 90°)

= 360° − 270°

= 90°

Therefore, the fourth angle is 90°.

Question 10: Why should the pencil be sharp during construction?

Solution:

A sharp pencil produces thin and accurate lines. Thick lines can make it difficult to identify exact intersection points and can reduce construction accuracy.

Question 11: Construct a quadrilateral using two adjacent sides and three given angles.

Solution:

1. Draw one of the given sides.
2. At its endpoint, construct the first given angle with a protractor.
3. Mark the second adjacent side on the ray.
4. At the next vertex, construct the second given angle.
5. Continue the construction using the third given angle.
6. Join the remaining points.
7. The required quadrilateral is obtained.

Question 12: What happens when a quadrilateral is divided by a diagonal?

Solution:

A diagonal divides the quadrilateral into two triangles.

Quadrilateral → 2 Triangles

Since each triangle has an angle sum of 180°, the total angle sum of the quadrilateral is 360°.

Question 13: What is the use of a ruler in practical geometry?

Solution:

A ruler is used to draw straight line segments and measure their lengths. It is important to keep the ruler properly aligned with the points while drawing a line.

Question 14: A quadrilateral has angles 75°, 85°, 110° and x°. Find x.

Solution:

We know:

75° + 85° + 110° + x = 360°

Therefore:

x = 360° − (75° + 85° + 110°)

x = 360° − 270°

x = 90°

Hence, the fourth angle is 90°.

Question 15: Write the correct order for constructing a quadrilateral using a diagonal.

Solution:

The general order is:

1. Identify the given measurements.
2. Choose a suitable diagonal.
3. Draw the diagonal accurately.
4. Use the given side lengths to draw arcs.
5. Locate the first unknown vertex.
6. Construct the second triangle on the other side of the diagonal.
7. Locate the second unknown vertex.
8. Join all the vertices.
9. Verify the construction.

Important Notes for Class 8 Practical Geometry

• Read the question carefully before beginning the construction.
• Always identify which measurements are given.
• Choose a suitable side or diagonal as the starting line.
• Use a sharp pencil for accurate lines and arcs.
• Do not change the compass opening while transferring a fixed length.
• Use the ruler carefully while measuring line segments.
• Use the protractor correctly when constructing angles.
• Construction arcs should be light but clearly visible.
• Do not erase important construction lines before the teacher checks them.
• Label all points clearly as A, B, C and D.
• Always check whether the final figure satisfies the measurements given in the question.

Common Mistakes to Avoid

• Using an incorrect scale while measuring a side.
• Changing the compass radius accidentally.
• Constructing an angle from the wrong side of a line.
• Joining the wrong intersection points.
• Forgetting to label the vertices.
• Making construction lines too dark.
• Starting the construction without understanding which measurement should be drawn first.
• Not checking the final quadrilateral against the given conditions.

Exam Tip: In a construction question, write the Steps of Construction clearly. Even if the diagram is correct, incomplete or unclear steps can make the solution difficult to understand.

Quick Revision Table

Concept	Important Point
Quadrilateral	Has 4 sides, 4 vertices and 4 angles
Interior angle sum	360°
Diagonal	Joins two non-adjacent vertices
Diagonal of quadrilateral	Divides it into two triangles
Ruler	Measures and draws line segments
Compass	Draws arcs and transfers lengths
Protractor	Measures and constructs angles
Construction	Requires accuracy and proper sequence

How to Score Better in Practical Geometry

To perform well in Class 8 Maths Practical Geometry, students should focus on accuracy rather than speed. First understand the given information and then decide which line segment should be drawn first.

Keep your instruments clean and use a sharp pencil. When using a compass, maintain the exact opening specified in the question. When using a protractor, make sure the centre of the protractor is placed exactly on the vertex of the angle.

During exams, always write the construction steps along with the diagram. Label the points properly and avoid unnecessary dark lines. A neat diagram makes the construction easier to check.

Practical Geometry – Exam Preparation Tips

• Practice constructions regularly instead of only reading the steps.
• Learn how to use a compass and protractor correctly.
• Practice drawing arcs with different radii.
• Understand why a diagonal is used to divide a quadrilateral into triangles.
• Memorise the angle sum of a quadrilateral: 360°.
• Practice construction questions with different combinations of sides and angles.
• Always verify the measurements after completing the figure.
• Keep your construction work neat and properly labelled.

Frequently Asked Questions – Practical Geometry Class 8

What is Practical Geometry in Class 8?

Practical Geometry is the study of constructing geometrical figures accurately using instruments such as a ruler, compass and protractor.

Which instruments are needed for Practical Geometry?

The main instruments are a ruler, compass and protractor. A pencil and eraser are also needed for neat construction.

How many diagonals does a quadrilateral have?

A quadrilateral has 2 diagonals. Each diagonal joins a pair of opposite vertices.

Why is a diagonal used while constructing a quadrilateral?

A diagonal divides the quadrilateral into two triangles. Triangles can be constructed more easily using known sides and angles.

What is the sum of the angles of a quadrilateral?

The sum of the interior angles of every quadrilateral is 360°.

Why is a compass important in construction?

A compass helps draw arcs and transfer exact lengths from one place to another.

What should I write in a construction question?

Write the construction steps clearly and draw a neat labelled diagram. Mention the measurements used at each important step.

How can I improve my Practical Geometry marks?

Practice regularly, use instruments accurately, keep diagrams neat, label all points and write complete construction steps.

Conclusion

Class 8 Practical Geometry teaches students how to construct quadrilaterals accurately using geometrical instruments. The most important ideas are understanding the given measurements, selecting a suitable starting line or diagonal, using arcs to locate unknown points, constructing angles correctly and joining the required vertices.

The key concept to remember is that a diagonal divides a quadrilateral into two triangles, which often makes construction easier. Students should also remember that the sum of the interior angles of a quadrilateral is 360°.

With regular practice, careful use of the ruler, compass and protractor, and properly written construction steps, Practical Geometry Class 8 becomes much easier and scoring.

Final Revision: Read the measurements → choose the starting side/diagonal → draw accurately → use arcs and angles → locate points → join vertices → verify the construction.

Disclaimer

This educational article is prepared for Class 8 Maths Practical Geometry revision and learning purposes. Construction methods may be presented in a simplified way for easy understanding. Students should also follow the exact instructions, diagrams and terminology given in their prescribed school textbook or by their teacher.