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CBSE Class 6 Mathematics Chapter 8 Playing with Constructions Worksheet with Answers

Welcome to the Playing with Constructions worksheet for CBSE Class 6 Mathematics Chapter 8. This chapter introduces you to the fascinating world of geometric constructions using compass and straight-edge — the same tools mathematicians have used for thousands of years. Through this worksheet, you will practice constructing line segments, circles, perpendicular bisectors, and triangles with precision. Each section progresses from basic recall to application and higher-order thinking. Complete this worksheet in approximately 60 minutes and check your answers against the detailed answer key provided at the end.

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Key takeaways

✓Compass and straight-edge are fundamental tools for accurate geometric constructions without relying on measurement scales
✓Perpendicular bisectors divide line segments into two equal parts at exactly 90 degrees using arc intersection methods
✓Triangles can be uniquely constructed when given three sides (SSS), two sides and included angle (SAS), or two angles and included side (ASA)
✓Circle construction requires fixing a center point and maintaining constant radius throughout the drawing motion
✓Line segment copying uses the compass to 'remember' and transfer exact distances from one location to another
✓Construction problems build spatial reasoning and prepare students for advanced geometry in higher classes
✓Regular practice with this worksheet improves precision, patience, and understanding of why geometric properties work

Quick Chapter Recap — Playing with Constructions

Chapter 8 Playing with Constructions from NCERT Class 6 Mathematics teaches students how to draw accurate geometric figures using only two tools: a compass and a straight-edge (ruler without markings). The compass is a V-shaped instrument with a needle at one end and a pencil at the other, used to draw circles and arcs and to transfer distances. The straight-edge is used solely to draw straight lines, not to measure lengths. The chapter covers several fundamental constructions. First, copying a given line segment by using the compass to 'remember' its length and transfer it to a new location. Second, drawing circles with a specified radius by fixing the compass needle at a center point and rotating the pencil around it. Third, constructing the perpendicular bisector of a line segment — a line that passes through the exact midpoint and meets the original segment at a right angle — by drawing arcs from both endpoints and connecting their intersection points. Finally, constructing triangles when given sufficient information: three sides (SSS construction), two sides and the included angle (SAS construction), or two angles and the included side (ASA construction). These constructions form the foundation for understanding geometric properties and spatial relationships. Mastering these skills develops precision, patience, and logical thinking. The constructions also reveal deep mathematical truths — for example, the perpendicular bisector construction proves that every point on that line is equidistant from the segment's endpoints.

Compass — tool to draw circles, arcs, and copy distances without measuring
Straight-edge — ruler used only for drawing straight lines, not for measuring
Line segment copying — transferring exact length using compass width
Circle construction — all points at fixed radius distance from center
Perpendicular bisector — line through midpoint at 90° to original segment
Triangle construction — SSS, SAS, and ASA methods create unique triangles

Worksheet Information and Instructions

This worksheet is designed for Class 6 students studying CBSE Mathematics Chapter 8 Playing with Constructions. It contains five distinct sections with varying difficulty levels, plus one case-study question that tests real-world application. The estimated completion time is 60 minutes, though students may take longer if they are practicing constructions for the first time. Difficulty level: Moderate, mixing recall, application, and higher-order thinking. Before starting, ensure you have a sharp pencil, eraser, compass with firm joints, and a transparent ruler for drawing straight lines. All constructions should be done neatly with clear arc marks visible. Do not erase construction arcs and lines — they are part of your working and demonstrate your method. For multiple-choice questions, select the single best answer. For fill-in-the-blanks, write the exact technical term. For short-answer questions, show step-by-step construction methods. For long-answer questions, provide complete constructions with all steps and reasoning. The case-study question requires reading a scenario and answering sub-questions based on construction concepts. After completing all sections, check your work against the comprehensive answer key provided. Each answer includes a brief explanation to help you understand any mistakes. This worksheet aligns with NCERT Class 6 Mathematics and CBSE examination patterns, making it excellent preparation for periodic tests and annual exams.

Total sections: Five main sections (A to E) plus one case study
Time allocation: 60 minutes total; spend more time on Section E
Materials needed: Pencil, eraser, compass, straight-edge ruler
Difficulty: Moderate, covering remembering to creating/evaluating levels
Instructions: Show all construction marks; do not erase working arcs
Marking: Each question carries marks indicated; total 50 marks

Section A — Multiple Choice Questions (1 mark each)

This section tests your understanding of basic concepts, terminology, and properties related to geometric constructions. Read each question carefully and select the single most appropriate answer from the four options provided. Remember that in construction geometry, precision and correct technique matter more than speed. Each MCQ is designed to check whether you understand the purpose of tools, the steps in standard constructions, and the geometric principles underlying each method. Some questions may include diagrams or descriptions of construction steps, requiring you to identify errors or predict outcomes. Do not guess randomly — eliminate obviously incorrect options first, then choose from the remaining alternatives. Even if a construction seems to 'look right', the mathematically correct method is what counts. Pay special attention to questions about the perpendicular bisector construction, as students often confuse it with simply finding the midpoint. Also note questions about triangle construction criteria — remember that three angles alone (AAA) do not uniquely determine a triangle's size, only its shape. These MCQs mirror the pattern of questions asked in CBSE periodic assessments and help build quick recall of essential facts. After completing this section, you should be confident about tool functions, construction vocabulary, and the logical sequence of steps in standard constructions taught in NCERT Class 6 Mathematics Chapter 8.

Section B — Fill in the Blanks (1 mark each)

Fill in the blanks with appropriate words or phrases from your study of Playing with Constructions. This section assesses your grasp of precise geometric terminology and definitions used in NCERT Class 6 Mathematics. Construction geometry has its own specialized vocabulary, and using the correct terms is essential for clear communication of mathematical ideas. Some blanks require tool names, others require construction terms like 'radius', 'bisector', or 'perpendicular'. A few statements describe properties or steps in construction methods — you must supply the missing word that completes the sentence accurately. Be specific: for example, 'a tool' is too vague when the answer should be 'compass'. Write neatly in the space provided. Spelling matters, especially for technical terms. If you are unsure, think about the context — is the sentence describing a tool, a property, a construction step, or a geometric figure? These fill-in-the-blank questions often appear in CBSE school exams because they efficiently test whether students have learned and can recall exact definitions and terms. Unlike MCQs where you can sometimes guess, fill-in-the-blanks require you to actively produce the correct term from memory. This strengthens retention and ensures you are building a solid foundation in geometric language. Review your NCERT textbook glossary and key concept boxes if you find this section challenging.

Section C — True or False (1 mark each)

Read each statement carefully and write 'True' if it is correct or 'False' if it is incorrect. This section tests your ability to distinguish accurate geometric facts from common misconceptions about constructions. Some statements are obviously true or false, while others are subtle and require you to think about the exact definitions and properties you have learned. For instance, a statement might say 'A compass can be used to measure angles' — this is false because a compass draws circles and copies distances, while a protractor measures angles. Another statement might claim 'Three angles are sufficient to construct a unique triangle' — this is also false because three angles determine shape but not size; infinitely many triangles can have the same three angles. Pay special attention to words like 'always', 'never', 'only', 'must', and 'can' — these qualifiers often make the difference between a true and false statement. Do not overthink: rely on what you have learned from NCERT Class 6 Mathematics Chapter 8. If a statement contradicts a construction method or property explained in your textbook, it is false. This question type appears frequently in CBSE assessments because it checks conceptual clarity quickly. After marking True or False, mentally explain why you chose that answer — this self-check reinforces understanding and prepares you for short-answer justifications.

Section D — Short Answer Questions (2 marks each)

Answer the following questions briefly but completely. Each question is worth 2 marks, so provide enough detail to demonstrate understanding. For questions asking you to list steps, write them in correct sequential order with clear numbering. For questions asking you to explain a concept, define the term first, then elaborate with an example or property. Short-answer questions in CBSE exams typically expect answers of 30 to 50 words or 3 to 5 well-organized points. Use proper geometric vocabulary — words like 'arc', 'radius', 'perpendicular', 'bisector', 'intersection', and 'segment' should appear naturally in your answers. If a question asks 'What is the use of a compass?', do not just write 'to draw circles'. Instead, write 'A compass is used to draw circles with a fixed radius, to draw arcs, and to copy or transfer distances from one location to another without measuring.' This shows deeper understanding. Some questions may ask you to describe a construction method — write the steps clearly and mention the tools used at each stage. Remember that constructions are about precision and following correct procedures, not rough sketches. If the question asks 'Why must the compass width be more than half the segment when constructing a perpendicular bisector?', explain that this ensures the arcs drawn from both endpoints will intersect above and below the segment, which is necessary to define the perpendicular bisector line. Practicing these short-answer questions strengthens your ability to communicate mathematical reasoning clearly, an essential skill for higher classes and competitive exams.

Section E — Long Answer and HOTS Questions (4 marks each)

This section contains long-answer and higher-order thinking skill (HOTS) questions that require detailed responses, construction diagrams, or multi-step reasoning. Each question is worth 4 marks, so take your time and show all working. For construction questions, draw neat diagrams with a sharp pencil, show all arcs and construction lines clearly, and label points properly. Do not erase your working — teachers award marks for correct construction steps even if the final figure is slightly inaccurate due to instrumental error. For reasoning questions, structure your answer logically: state what is given, what you need to find or prove, then work through the solution step by step. HOTS questions may ask you to apply constructions in unfamiliar contexts, compare methods, identify errors in given constructions, or explain why certain constructions are impossible. For example, you might be asked 'Can you construct a triangle with sides 3 cm, 4 cm, and 10 cm? Explain with reasoning.' The answer is no, because the sum of two shorter sides (3 + 4 = 7 cm) is less than the third side (10 cm), violating the triangle inequality property. Such questions go beyond rote memorization and test whether you truly understand the underlying principles. When describing construction steps, use imperative sentences: 'Draw a line segment AB', 'Set compass to radius 4 cm', 'Place compass needle at point A', 'Draw an arc above the line'. Number your steps for clarity. If the question asks you to construct and then measure something, do the construction first accurately, then use your ruler or protractor to measure and report the value. These questions reflect the kind of problems asked in CBSE annual exams and Olympiad-level assessments, making them excellent practice for high achievement.

Section F — Case Study Question (1+1+2 = 4 marks)

Read the following case study carefully and answer the questions that follow. Case-study questions are a recent addition to CBSE question papers and test your ability to apply mathematical concepts to real-life scenarios. The case study will describe a practical situation involving constructions — for example, a carpenter marking wood, an architect planning a layout, or an artist creating a design. You will then answer 2 to 3 sub-questions based on that scenario. The first sub-question is usually straightforward recall or identification (1 mark). The second tests application (1 mark). The third requires deeper reasoning or a multi-step solution (2 marks). When answering, refer back to the case-study text and use the information provided. Do not make assumptions beyond what is stated. If the case study mentions specific measurements or constraints, incorporate them into your answers. For instance, if a gardener needs to mark the center of a circular flower bed, you would explain that the center is the point from which all boundary points are equidistant (radius), and you could locate it by drawing two chords and constructing their perpendicular bisectors — their intersection is the center. Case-study questions encourage you to see how geometric constructions are not just abstract exercises but tools used by professionals in various fields. They also test reading comprehension alongside mathematical skills, so read the passage twice before attempting the sub-questions.

Answer Key — Section A (MCQs)

Here are the correct answers to all multiple-choice questions in Section A with brief explanations. Each MCQ carried 1 mark. Check your responses and read the explanations for any questions you answered incorrectly. Understanding why an answer is correct is more important than simply knowing the answer. If you scored less than 6 out of 8, revisit the relevant sections of NCERT Class 6 Mathematics Chapter 8 and practice similar questions. MCQs test quick recall and conceptual clarity, both essential for doing well in CBSE periodic tests and annual exams. Note the reasoning provided for each answer — this helps you avoid similar mistakes in future assessments and builds a stronger mental model of construction concepts. If you got a question wrong, write the correct answer three times and the explanation once in your notebook. This reinforcement technique significantly improves retention and exam performance.

1. (c) Compass — The compass is the primary tool for drawing circles and arcs with a fixed radius.
2. (b) Draw straight lines only — A straight-edge has no markings and is not used for measurement, only for joining points.
3. (c) Two equal parts at 90° — A perpendicular bisector divides a segment into two equal halves and meets it at a right angle.
4. (b) Radius — To construct a circle, you must know the radius (distance from center to circumference).
5. (c) More than half of AB — This ensures arcs from A and B intersect both above and below the segment.
6. (b) Three sides only — Knowing all three sides (SSS) uniquely determines one triangle. Three angles (AAA) only determine shape, not size.
7. (a) Side-Side-Side — SSS is a triangle construction criterion meaning all three side lengths are given.
8. (b) Intersection point — The point where two arcs cross is called the intersection point, used to define new locations.

Answer Key — Sections B, C, D, E, F

This section provides detailed answers and explanations for all remaining questions: fill-in-the-blanks, true/false, short-answer, long-answer HOTS questions, and the case-study question. Each answer includes not only the correct response but also reasoning or step-by-step working where applicable. For construction questions, written steps are provided since diagrams cannot be shown in text format — when practicing, always draw the actual figures on paper. For short-answer questions, the explanations are slightly expanded beyond the minimum required so you understand the concept fully. For HOTS questions, multiple approaches are sometimes discussed to show different ways of thinking about the same problem. If your answer matches the key conceptually but uses slightly different wording, you should still award yourself full marks — mathematics is about understanding, not memorizing exact phrases. However, if your construction steps were in the wrong order or you missed a critical step, review that construction method again from your NCERT textbook. Use this answer key not just to score your work, but as a learning tool. Read through all explanations even for questions you answered correctly, as they often contain insights and connections that deepen understanding. If you are preparing for CBSE exams, pay special attention to the wording and level of detail in these answers — this shows you what examiners expect in a full-credit response. For any topic where you lost marks, create a personalized revision note summarizing the concept, the correct method, and a reminder of what to watch out for. Consistent review and self-correction are the keys to mastery in geometry.

Section B answers: 1. compass, 2. markings, 3. radius, 4. bisector, 5. ninety (or 90), 6. compass, 7. sides, 8. center
Section C answers: 1. False, 2. True, 3. False, 4. False, 5. False, 6. True, 7. True, 8. True
Section D sample answer for Q1: The two main tools are compass (used to draw circles, arcs, and copy distances) and straight-edge (used to draw straight lines only, without measurement).
Section D sample answer for Q4: A perpendicular bisector is a line that divides a line segment into two equal parts and is perpendicular (at 90°) to it. Important property: Every point on the perpendicular bisector is equidistant from the two endpoints of the segment.
Section E sample answer for Q3: The student's mistake was setting compass width to exactly half of CD. For perpendicular bisector construction, compass width must be MORE than half the segment length so arcs from both ends intersect above and below the line. Correct method: Set compass to radius > CD/2, place at C and draw arcs above and below, then place at D with same width and draw arcs crossing the first arcs, join intersection points.
Section F case-study answers: (i) Using scale 1 cm = 10 m, side lengths are 8 cm, 6 cm, and 7 cm. (ii) Rahul should use SSS construction because all three side lengths are given. (iii) Steps: Draw base AB = 8 cm. Set compass to 7 cm, place at A, draw arc above line. Set compass to 6 cm, place at B, draw arc to intersect first arc at C. Join AC and BC to complete triangle.

How CBSETUTOR.ai Supports Your Construction Practice

Geometric constructions require not just theoretical knowledge but hands-on practice and immediate feedback — both of which are challenging in traditional self-study. CBSETUTOR.ai offers a powerful solution for CBSE Class 6 students mastering Playing with Constructions. The platform provides 24×7 access to an AI tutor that can clarify doubts about construction steps, explain why certain methods work, and guide you through tricky problems. If you are stuck on a construction question, simply upload a photo of your attempt using the app. The AI analyses your working, identifies where you went wrong (for example, incorrect compass width or missing construction arcs), and provides step-by-step correction guidance. This is especially valuable for constructions because small errors in one step cascade into incorrect final figures. The platform also generates unlimited practice worksheets similar to this one, with varying difficulty levels and question types. You can practice SSS, SAS, and ASA triangle constructions repeatedly until you achieve fluency. Parents appreciate the flat pricing — ₹999 per month covers every subject and every CBSE class from 6 to 12, making it affordable for families with multiple children. A 3-day free trial lets you explore the platform's features risk-free. Beyond worksheets, CBSETUTOR.ai includes chapter-wise video explanations, interactive quizzes, and exam preparation modules aligned with the latest CBSE syllabus. For Chapter 8, you will find animated demonstrations of each construction, showing exactly how to hold the compass, where to place the needle, and how to ensure your arcs intersect correctly. The AI tutor patiently answers conceptual questions like 'Why does the perpendicular bisector construction work?' or 'Can I construct a triangle with sides 2 cm, 3 cm, and 6 cm?' with detailed mathematical reasoning. This instant, personalized support transforms learning from frustrating trial-and-error into confident, guided skill-building. Whether you are revising before a periodic test or building a strong foundation for future geometry topics, CBSETUTOR.ai is the ideal learning partner for NCERT Class 6 Mathematics and beyond.

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Frequently asked questions

What is the difficulty level and suggested time for this worksheet?+

This worksheet is of moderate difficulty, suitable for Class 6 students who have completed Chapter 8. The suggested time is 60 minutes, allowing approximately 8 minutes for Section A, 6 minutes for Section B, 5 minutes for Section C, 14 minutes for Section D, 20 minutes for Section E, and 7 minutes for the case study. Students new to constructions may take longer initially.

Do I need to show construction arcs in my answers?+

Yes, absolutely. Construction arcs and working lines are part of your method and carry marks in CBSE exams. Never erase them after completing the figure. Examiners award credit for correct construction steps even if the final figure has minor inaccuracies. Clear, visible arcs demonstrate that you followed the proper geometric procedure rather than guessing or measuring.

What is the most common mistake students make in perpendicular bisector construction?+

The most common mistake is setting the compass width to exactly half (or less than half) of the line segment. This causes the arcs from both endpoints to not intersect above and below the line. The compass width must be MORE than half the segment length to ensure the arcs cross at two points, which are then joined to form the perpendicular bisector.

Can I use a ruler to measure lengths during construction?+

For copying existing segments or when a specific length is given (like 'construct a segment of 7 cm'), you may initially measure with a ruler. However, the essence of geometric construction is transferring lengths using the compass without repeated measuring. Once you set the compass to a length, you should use it to mark that length elsewhere. During exams, show the compass transfer method in your working.

Why can we not construct a unique triangle with three angles only?+

Three angles determine the shape of a triangle but not its size. For example, all triangles with angles 60°-60°-60° are equilateral, but they can be tiny or huge. Infinitely many triangles can have the same three angles but different side lengths. To construct a unique triangle, you need at least one side length along with angles, or you need all three sides (SSS).

What materials do I need to complete this worksheet?+

You need a sharp HB or 2B pencil, a good eraser, a compass with a firm joint that holds its width, and a transparent ruler (straight-edge). Ensure your compass pencil is sharp and level with the needle point. A geometry box is ideal. For best results, use unruled white paper. Avoid using pens for constructions as mistakes cannot be corrected easily.

How is this worksheet aligned with CBSE exam patterns?+

This worksheet mirrors the variety and difficulty of questions in CBSE periodic tests and annual exams. It includes MCQs and fill-in-the-blanks for objective assessment, short-answer questions for method demonstration, long-answer HOTS questions for deeper application, and a case-study question reflecting the latest CBSE question paper format. Practicing these question types builds comprehensive exam readiness for Class 6 Mathematics.

Where can I find step-by-step solutions if I get stuck?+

The complete answer key section at the end of this worksheet provides detailed solutions and explanations for every question. For additional help, CBSETUTOR.ai offers 24×7 AI tutor support. You can upload a photo of your construction attempt and receive personalized feedback on errors and corrections. The platform also has animated video demonstrations of each construction method from Chapter 8.

Are there more practice worksheets available for Playing with Constructions?+

Yes, CBSETUTOR.ai generates unlimited practice worksheets for CBSE Class 6 Mathematics Chapter 8 and all other chapters. Each worksheet has different questions while maintaining NCERT syllabus alignment and CBSE exam patterns. This allows for repeated practice until you achieve full confidence. A 3-day free trial gives you access to the complete worksheet library for all subjects and classes.

What should I do if my constructed triangle does not close properly?+

If your triangle sides do not meet at the third vertex, check these common errors: incorrect compass width (recheck the given measurements), compass slipping (tighten the joint), or choosing the wrong intersection point of arcs (pick the intersection that makes geometric sense). Also verify that the three given sides satisfy the triangle inequality — the sum of any two sides must be greater than the third side. If they do not, a triangle cannot be constructed.

Related resources

Important Questions: CBSE Class 6 Mathematics Chapter 8 Playing with Constructions Class 6 Mathematics Chapter 8 Playing with Constructions — Formulas & Key Points NCERT Solutions for CBSE Class 6 Mathematics Chapter 8: Playing with Constructions CBSE Class 6 Mathematics Chapter 8 Playing with Constructions — Notes AI Tutor for Class 6: The Smart Alternative to Tuition AI Tutor for Class 6 Maths: Learn Faster with Instant Help NCERT Solutions for Class 9 Mathematics Chapter 1: Number Systems – Complete Guide CBSE Class 9 Mathematics Chapter 1 Number Systems Worksheet with Answers

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