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NCERT Solutions for CBSE Class 6 Mathematics Chapter 8: Playing with Constructions

CBSE Class 6 Mathematics Chapter 8 Playing with Constructions is where geometry comes alive through your own hands. Unlike earlier chapters that focused on numbers and arithmetic, this chapter equips you with a compass and straight-edge to draw exact geometric figures — line segments, circles, perpendicular bisectors, and triangles. These constructions are not approximations; they are mathematically perfect. The 2024-25 NCERT syllabus for Class 6 Mathematics dedicates this chapter to building spatial reasoning and precision, skills that form the backbone of geometry in Classes 7, 8, 9, and 10. Every CBSE board exam from Class 9 onwards includes construction questions worth 6–8 marks, making this chapter a critical foundation. This guide provides complete NCERT solutions for CBSE Class 6 Mathematics Chapter 8 Playing with Constructions, with step-by-step methods, worked examples, and strategies to avoid the most common mistakes students make during exams.

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Key takeaways

  • ✓CBSE Class 6 Mathematics Chapter 8 Playing with Constructions teaches compass-and-straight-edge geometry, forming the basis of all higher-level constructions in Classes 7–10.
  • ✓The compass 'remembers' distances: once set to a given length, it can replicate that exact length anywhere on the page without a ruler.
  • ✓Perpendicular bisector construction requires compass width greater than half the segment length; otherwise arcs will not intersect on both sides.
  • ✓Three methods uniquely determine a triangle: SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side) — all tested in CBSE exams.
  • ✓Every point on a perpendicular bisector is equidistant from the segment's endpoints, a property used in real-world applications like network design and architecture.
  • ✓CBSE Class 6 Mathematics Chapter 8 exercises emphasize construction over measurement, training students to think geometrically rather than arithmetically.
  • ✓Accurate constructions demand sharp pencils, clear arcs, and patience — skills that improve with practice and directly impact marks in practical geometry questions.

Understanding the Tools: Compass and Straight-Edge in CBSE Class 6 Mathematics Chapter 8

CBSE Class 6 Mathematics Chapter 8 Playing with Constructions introduces two essential tools that every geometry student must master: the compass and the straight-edge. A compass is a V-shaped instrument with a sharp needle on one arm and a pencil holder on the other. When you open the compass to a specific width and place the needle at a point, the pencil draws a circle (or arc) where every point is exactly the same distance — the radius — from the center. This property makes the compass indispensable for copying distances and drawing circles. A straight-edge, often called an unmarked ruler, is used solely to draw straight lines between two points; it has no measurement markings and must never be used for measuring lengths. The NCERT textbook for Class 6 Mathematics Chapter 8 emphasizes that constructions must rely on geometric relationships, not on ruler measurements. This trains students to think about why shapes have certain properties rather than simply measuring and drawing. In ancient Greek mathematics, the compass-and-straight-edge restriction led to profound discoveries about which constructions are possible (trisecting an angle is impossible, for example). For CBSE students, mastering these tools in Class 6 builds the foundation for all construction questions in Classes 7–10, where marks are awarded for both accuracy and method. During exams, use a sharp pencil in your compass to ensure arcs are visible and intersection points are clear.
  • Compass — opens to a fixed width, draws circles or arcs, 'remembers' distances without measuring
  • Straight-edge — draws straight lines only, has no measurement markings, never used for measuring distances
  • Construction philosophy — geometric relationships over arithmetic measurement, training spatial reasoning
  • Historical context — ancient Greek mathematicians proved some constructions impossible with these tools alone
  • Exam relevance — CBSE board exams from Class 9 onwards allocate 6–8 marks to construction questions

Constructing Line Segments: Copying Lengths Without Measuring

One of the first skills taught in CBSE Class 6 Mathematics Chapter 8 Playing with Constructions is how to copy a given line segment to a new location without using a ruler to measure its length. This construction demonstrates the core principle of geometric construction: the compass can transfer distances perfectly. Imagine you are given a line segment AB and asked to construct another segment CD of exactly the same length. Place the compass needle at point A and open the pencil arm until it touches point B — the compass now 'holds' the length AB in its width. Without changing this width, place the needle at the new starting point C and swing the pencil to mark point D on the line you have drawn. The segment CD is now identical in length to AB. This method works because the compass maintains a constant radius; both segments span the same distance. In the NCERT textbook for Class 6 Mathematics Chapter 8, students practice this construction with segments of various lengths, building the muscle memory needed for more complex constructions. The technique is tested in school exams where a segment of unknown length is given, and students must replicate it elsewhere on the page. Common mistakes include accidentally shifting the compass width before marking point D or drawing the arc too faintly to see where it crosses the line. Always draw arcs with enough pressure to make them visible, and double-check that the compass has not slipped before marking the second point.

Drawing Circles and Understanding Radius in Playing with Constructions

CBSE Class 6 Mathematics Chapter 8 Playing with Constructions teaches that a circle is the set of all points at a fixed distance (the radius) from a center point. The compass is the perfect tool for drawing circles because its needle marks the center and its pencil traces every point at radius distance. To construct a circle with center O and radius r, mark the center point O on your page, set the compass width to the desired radius (either by measuring against a given segment or opening it to a specific width if you have a ruler for reference), place the needle firmly at O, and rotate the pencil around the center while keeping the width constant. The curve you trace is a perfect circle. Every point on this circle is exactly r units from O. In the NCERT textbook for Class 6 Mathematics Chapter 8, students practice drawing circles with different radii and learn to identify key parts: the center, radius, diameter (twice the radius), circumference (the boundary), and interior. Questions in CBSE exams often ask students to construct a circle with a given radius and then mark specific points on it, verifying that all points are equidistant from the center. A common mistake is allowing the compass to slip during rotation, which creates an oval instead of a circle. To prevent this, hold the compass by the top knob and rotate smoothly without applying downward pressure that might change the width. Another error is placing the needle off-center, resulting in a circle that does not pass through the intended points.
  • Circle definition — set of all points at a constant distance (radius) from a center point O
  • Compass as circle-drawer — needle at center, pencil traces all points at radius r
  • Key parts — center O, radius r, diameter 2r, circumference (boundary), interior (inside the circle)
  • Exam construction — 'Draw a circle with center A and radius 5 cm' is a standard 2-mark question
  • Common error — compass slipping during rotation, producing an oval; hold the top knob and rotate smoothly

Perpendicular Bisector Construction: Dividing Segments into Equal Halves

The perpendicular bisector is one of the most important constructions in CBSE Class 6 Mathematics Chapter 8 Playing with Constructions. A perpendicular bisector of a line segment is a line that passes through the segment's midpoint and meets it at a right angle (90 degrees). This construction has a remarkable property: every point on the perpendicular bisector is equidistant from the segment's two endpoints. To construct the perpendicular bisector of segment AB, set your compass to a width greater than half the length of AB — this is crucial. Place the needle at point A and draw arcs both above and below the line. Without changing the compass width, place the needle at point B and draw arcs above and below that cross the first arcs. The arcs intersect at two points; call them P (above) and Q (below). Draw a straight line through P and Q using the straight-edge. This line PQ is the perpendicular bisector of AB. It crosses AB at its exact midpoint M, and angle AMQ (or angle BMQ) is exactly 90 degrees. The NCERT textbook for Class 6 Mathematics Chapter 8 provides multiple exercises where students construct perpendicular bisectors and verify the midpoint by measurement afterward. In CBSE school exams, this construction is tested frequently, often combined with other steps like constructing a triangle and then bisecting one of its sides. The most common mistake is setting the compass width to less than half the segment length, which causes the arcs from A and B not to intersect on both sides. Always open the compass generously — a good rule of thumb is to set it to about three-quarters of the segment length.

Why the Perpendicular Bisector Works: Equidistance Property

A deep understanding of why the perpendicular bisector construction works is essential for mastering CBSE Class 6 Mathematics Chapter 8 Playing with Constructions. When you draw arcs from both endpoints A and B with the same compass width (radius r), you are identifying all points that are exactly r units from A and all points that are exactly r units from B. The two arcs intersect at points P and Q, which are the only points in the plane that are equidistant from both A and B. By definition, any point that is equidistant from two fixed points must lie on the perpendicular bisector of the segment joining those points. This is a fundamental theorem in geometry: the locus of points equidistant from two points is the perpendicular bisector. Therefore, the line PQ is guaranteed to be perpendicular to AB and to pass through its midpoint. This property is not just theoretical; it has practical applications in real life. For example, if two villages A and B want to build a shared water pump, the ideal location is on the perpendicular bisector of the segment AB so that both villages are equally far from the pump. In CBSE exams, students are sometimes asked to explain why the construction produces a perpendicular bisector rather than just following steps mechanically. Being able to articulate the equidistance property earns full marks on such questions and demonstrates conceptual understanding.
  • Equidistance theorem — any point equidistant from A and B lies on the perpendicular bisector of AB
  • Construction logic — arcs from A and B with same radius intersect at points P and Q, both equidistant from A and B
  • Perpendicularity — line PQ is perpendicular to AB because of symmetry; both halves mirror each other
  • Midpoint property — PQ crosses AB at M, where AM = MB, making M the exact midpoint
  • Real-world application — locating a facility equidistant from two towns, designing balanced structures

Triangle Construction Method 1: Three Sides Given (SSS Construction)

CBSE Class 6 Mathematics Chapter 8 Playing with Constructions introduces triangle construction using the SSS method, where all three side lengths are given. A triangle is uniquely determined if you know the lengths of all three sides (provided they satisfy the triangle inequality: the sum of any two sides must be greater than the third side). To construct a triangle with sides of length a, b, and c, start by drawing a line segment equal to one side — say AB = a. Next, set your compass to the length of the second side (b) and place the needle at point A. Draw an arc above the line AB. Without changing the compass, set it to the third side length (c), place the needle at point B, and draw another arc that intersects the first arc. Mark the intersection point as C. Finally, use the straight-edge to join A to C and B to C. Triangle ABC now has sides AB = a, AC = b, and BC = c. The NCERT textbook for Class 6 Mathematics Chapter 8 provides several exercises where students are given three side lengths and must construct the triangle accurately. This construction is tested extensively in CBSE exams, often worth 3–5 marks. Students must show all construction arcs clearly and label points correctly to earn full marks. A common mistake is drawing the arc from only one endpoint, which does not uniquely locate point C. Always draw arcs from both A and B so their intersection determines the third vertex. Another error is violating the triangle inequality (for example, trying to construct a triangle with sides 2 cm, 3 cm, and 6 cm), which is impossible because 2 + 3 is not greater than 6.

Triangle Construction Method 2: Two Sides and Included Angle (SAS Construction)

Another essential method covered in CBSE Class 6 Mathematics Chapter 8 Playing with Constructions is SAS (Side-Angle-Side) construction, where two side lengths and the angle between them are given. To construct a triangle with sides AB = a, AC = b, and the included angle at A equal to θ degrees, first draw a line segment AB = a. At point A, use a protractor to construct an angle of θ degrees. Draw a ray from A along this angle direction. On this ray, measure and mark point C such that AC = b. Finally, join B to C using the straight-edge. Triangle ABC is now complete with AB = a, AC = b, and angle BAC = θ. The NCERT textbook for Class 6 Mathematics Chapter 8 emphasizes that the angle must be the included angle (the angle between the two given sides). If the angle is not between the two sides, the triangle is not uniquely determined, and the construction may fail or produce multiple solutions. In CBSE school exams, SAS construction questions typically provide two side lengths in centimeters and an angle in degrees. Students must construct the angle accurately using a protractor, mark the second side length precisely, and join the points cleanly. A common mistake is measuring the angle from the wrong baseline or placing point C on the wrong ray. Always ensure the protractor's center is exactly at point A and the baseline aligns with AB before marking the angle.

Common Mistakes in CBSE Class 6 Mathematics Chapter 8 Constructions

Students preparing for exams on CBSE Class 6 Mathematics Chapter 8 Playing with Constructions often make recurring mistakes that cost them marks. The most frequent error is setting the compass width incorrectly when constructing a perpendicular bisector. If the compass is opened to less than half the segment length, the arcs from the two endpoints will not intersect on both sides, making it impossible to locate the bisector. Always set the compass to more than half — a safe choice is three-quarters of the segment length. Another common mistake is changing the compass width mid-construction. For example, when drawing arcs from points A and B to locate the perpendicular bisector, the compass must maintain the same width for both arcs. If you accidentally adjust the compass between arcs, the resulting line will not be perpendicular or pass through the midpoint. A third error is drawing arcs too lightly or too small. Intersection points must be clearly visible; faint arcs make it difficult to locate where arcs cross, leading to inaccurate constructions. Use a sharp pencil and press firmly enough to leave a visible mark. In triangle constructions, students sometimes violate the triangle inequality, attempting to construct a triangle with sides that cannot form a closed shape (for example, sides 2 cm, 3 cm, and 6 cm). Before starting, check that the sum of any two sides is greater than the third. Finally, failing to label points clearly or omitting construction arcs in the final diagram can result in lost marks even if the construction is correct. CBSE examiners expect to see all working, including arcs and labeled vertices.
  • Compass too narrow for perpendicular bisector — arcs will not intersect; always open compass to more than half the segment
  • Changing compass width mid-construction — breaks symmetry; keep compass fixed once set
  • Light or small arcs — intersection points invisible; draw arcs firmly with a sharp pencil
  • Triangle inequality violation — attempting impossible constructions; verify sum of two sides exceeds the third before starting
  • Missing labels or arcs in final diagram — examiner cannot verify method; show all construction lines and label clearly

Step-by-Step Solution: NCERT Exercise 8.1 Question on Copying a Line Segment

NCERT Exercise 8.1 in CBSE Class 6 Mathematics Chapter 8 Playing with Constructions typically begins with a question asking students to copy a given line segment. A representative question is: 'You are given a line segment PQ. Construct a line segment RS of the same length using compass and straight-edge.' Here is the complete step-by-step solution. Step 1: Observe the given segment PQ and draw a long straight line on which segment RS will be constructed. Mark a point R on this line. Step 2: Place the compass needle at point P and open the pencil arm until it touches point Q. The compass now holds the length PQ in its width. Ensure the compass is tight so the width does not change. Step 3: Without altering the compass width, place the needle at point R (the starting point of the new segment). Step 4: Swing the compass pencil to draw an arc that crosses the line. Mark the intersection of the arc with the line as point S. Step 5: Segment RS is now equal in length to segment PQ. Verification: To check your work, place the compass needle at R and pencil at S; the width should match the original PQ length. This construction reinforces the fundamental principle that the compass can transfer distances perfectly without measurement. Students should practice this construction multiple times with segments of different lengths to build confidence and accuracy. In exams, this question is usually worth 2–3 marks, with marks awarded for correct method (showing arcs and labeled points) and accurate result.
  • Step 1 — Draw a new line, mark starting point R
  • Step 2 — Compass needle at P, pencil at Q, 'hold' the length PQ
  • Step 3 — Needle at R without changing compass width
  • Step 4 — Draw arc crossing the line, mark intersection as S
  • Step 5 — RS equals PQ; verify by checking compass holds same width from R to S

Step-by-Step Solution: NCERT Exercise 8.2 Question on Constructing a Circle

A typical question from NCERT Exercise 8.2 in CBSE Class 6 Mathematics Chapter 8 Playing with Constructions asks students to draw a circle with a specified center and radius. For example: 'Construct a circle with center O and radius 4 cm. Mark any two points P and Q on the circle and verify that OP = OQ = 4 cm.' Here is the detailed solution. Step 1: Mark a point O on your page; this will be the center of the circle. Write the letter O clearly next to the point. Step 2: Set your compass to a width of 4 cm. You can do this by placing the compass needle at the 0 mark of a ruler and opening the pencil arm until it reaches the 4 cm mark. Alternatively, if a line segment of 4 cm is given, set the compass to match that segment using the method from Exercise 8.1. Step 3: Place the compass needle firmly at point O. Ensure the needle does not slip; you may press it lightly into the paper. Step 4: Rotate the compass slowly and smoothly, keeping the needle fixed at O, until the pencil traces a complete curve back to the starting point. This curve is the circle with center O and radius 4 cm. Step 5: Mark two points P and Q anywhere on the circle. Use the straight-edge to join O to P and O to Q. Step 6: Verification: Measure OP and OQ using a ruler. Both should be exactly 4 cm because every point on the circle is at radius distance from the center. If the measurements are not 4 cm, the compass may have slipped during rotation. This exercise reinforces the definition of a circle and trains students to rotate the compass smoothly without changing its width. In CBSE exams, circle construction is often combined with other steps, such as drawing a chord or constructing tangents (in higher classes).

Step-by-Step Solution: NCERT Exercise 8.3 Question on Perpendicular Bisector

NCERT Exercise 8.3 in CBSE Class 6 Mathematics Chapter 8 Playing with Constructions focuses on perpendicular bisector construction. A sample question is: 'Draw a line segment AB of length 8 cm. Construct its perpendicular bisector. Mark the point where the bisector intersects AB as M. Measure AM and MB to verify that M is the midpoint.' Here is the complete solution. Step 1: Draw a horizontal line and mark point A. Using a ruler, measure 8 cm from A and mark point B. Draw a neat line segment AB. Step 2: Set your compass to a width greater than 4 cm (half of 8 cm). A good choice is 6 cm, which is more than half. Step 3: Place the compass needle at point A. Draw an arc above the line AB and another arc below the line AB. The arcs should extend well beyond the midpoint region. Step 4: Without changing the compass width (still 6 cm), place the needle at point B. Draw arcs above and below AB that intersect the arcs drawn from A. You should now see two clear intersection points. Step 5: Label the upper intersection point as P and the lower intersection point as Q. Step 6: Using the straight-edge, draw a straight line through points P and Q. This line is the perpendicular bisector of AB. Step 7: Mark the point where line PQ crosses segment AB as M. This is the midpoint of AB. Step 8: Verification: Measure AM and MB with a ruler. Both should be exactly 4 cm. Also, check that line PQ forms a right angle with AB by placing a set square at M. If AM ≠ MB, recheck that the compass width was kept constant and that arcs were drawn on both sides of AB. This construction is heavily tested in CBSE exams, often worth 4–5 marks, with marks awarded for clear arcs, correct labeling, and verification.
  • Step 1 — Draw AB = 8 cm clearly
  • Step 2 — Compass to 6 cm (more than half of 8 cm)
  • Step 3 — Needle at A, draw arcs above and below AB
  • Step 4 — Needle at B (same width), draw arcs crossing the first arcs
  • Step 5 — Label intersections as P and Q
  • Step 6 — Draw line PQ (the perpendicular bisector)
  • Step 7 — Mark M where PQ crosses AB (the midpoint)
  • Step 8 — Verify AM = MB = 4 cm and angle AMQ = 90°

Step-by-Step Solution: NCERT Exercise 8.4 Question on Triangle Construction (SSS)

NCERT Exercise 8.4 in CBSE Class 6 Mathematics Chapter 8 Playing with Constructions introduces triangle construction using the SSS method. A typical question is: 'Construct a triangle PQR with sides PQ = 5 cm, QR = 6 cm, and PR = 7 cm.' Here is the detailed solution. Step 1: Draw a horizontal line and mark point P. Using a ruler, measure 5 cm from P and mark point Q. Draw a clear line segment PQ = 5 cm. This will be the base of the triangle. Step 2: Set your compass to a width of 7 cm (the length of side PR). Place the needle at point P and draw a large arc above the line PQ. This arc represents all points that are 7 cm away from P. Step 3: Without changing the compass, set it to 6 cm (the length of side QR). Place the needle at point Q and draw another arc above the line PQ that intersects the first arc. This arc represents all points that are 6 cm away from Q. Step 4: Mark the intersection of the two arcs as point R. This point is uniquely determined because it is the only point that is exactly 7 cm from P and 6 cm from Q. Step 5: Using the straight-edge, draw a line segment from P to R and another from Q to R. Triangle PQR is now complete with sides PQ = 5 cm, QR = 6 cm, and PR = 7 cm. Step 6: Verification: Measure each side with a ruler to confirm the lengths. Also, ensure that the sum of any two sides is greater than the third side (triangle inequality). In this case, 5 + 6 > 7, 5 + 7 > 6, and 6 + 7 > 5, so the triangle is valid. This construction is one of the most important in CBSE Class 6 Mathematics Chapter 8 Playing with Constructions and is frequently tested in school exams with 4–5 marks allocated. Students must show all construction arcs clearly and label all vertices.

How CBSETUTOR.ai Helps Students Master Playing with Constructions

Mastering CBSE Class 6 Mathematics Chapter 8 Playing with Constructions requires patience, precision, and repeated practice — skills that can be challenging to develop through textbooks alone. This is where CBSETUTOR.ai becomes invaluable. CBSETUTOR.ai is India's first 24×7 AI tutor designed exclusively for CBSE students in Classes 6–12. It has ingested every NCERT textbook, including the complete Class 6 Mathematics curriculum, and can answer questions, explain constructions step-by-step, and even analyze photos of your attempted constructions to identify mistakes. For example, if a student is struggling with the perpendicular bisector construction, they can upload a photo of their work to CBSETUTOR.ai, and the AI will pinpoint errors such as 'compass width too narrow' or 'arcs not drawn on both sides.' The platform also provides personalized practice problems tailored to each student's weak areas, ensuring that time is spent where it matters most. At just ₹999 per month for all classes 6–12, CBSETUTOR.ai is more affordable than a single private tutor session, yet it is available anytime a student needs help — early morning before school, late evening during homework, or weekends during exam preparation. The platform includes a 3-day free trial with no credit card required, allowing parents and students to experience the AI tutor risk-free. Thousands of CBSE families across India rely on CBSETUTOR.ai to clarify doubts instantly, build conceptual understanding, and improve exam performance. For a chapter like Playing with Constructions, where hands-on practice and immediate feedback are crucial, CBSETUTOR.ai's ability to analyze student work and provide corrective guidance is unmatched by traditional resources.
  • 24×7 AI tutor — available anytime for doubts, explanations, and step-by-step construction guidance
  • Photo upload feature — snap a picture of your construction, AI identifies errors and suggests corrections
  • NCERT-grounded — every explanation aligned with the 2024-25 CBSE Class 6 Mathematics syllabus
  • Personalized practice — AI generates custom problems targeting weak areas in constructions
  • Affordable — ₹999/month for all classes 6–12, far cheaper than private tutors
  • 3-day free trial — no credit card required, risk-free experience of the platform

Exam Preparation Strategy for CBSE Class 6 Mathematics Chapter 8 Playing with Constructions

Scoring well on CBSE Class 6 Mathematics Chapter 8 Playing with Constructions requires a structured preparation strategy. First, ensure your geometric tools are in good condition: a compass that holds its width without slipping, a sharp pencil, a clean straight-edge, and a protractor for angle constructions. Practice each construction type — copying line segments, drawing circles, perpendicular bisectors, and triangles — at least five times until you can complete each one smoothly and accurately. Time yourself; in exams, you will have limited time per question, so speed with accuracy is essential. Second, memorize the steps for each construction method (SSS, SAS, ASA) and understand the reasoning behind each step. CBSE examiners often ask 'Why does this construction work?' or 'What property ensures the bisector is perpendicular?' Be prepared to explain the equidistance property, the role of arcs, and the triangle inequality. Third, when practicing, always draw construction arcs clearly and label all points. In exams, even if your final figure is slightly inaccurate, you will earn partial marks if your method is correct and visible. Never erase construction arcs after completing the figure; they are evidence of your method. Fourth, solve all NCERT exercises (8.1 through 8.4) multiple times and attempt additional problems from reference books like R.S. Aggarwal or R.D. Sharma. Fifth, review common mistakes (narrow compass width, changing width mid-construction, faint arcs) and consciously avoid them. Finally, a week before the exam, do a full timed mock test covering all construction types. This will build confidence and ensure you can reproduce constructions under exam pressure. Students using CBSETUTOR.ai can upload their mock test constructions for AI-powered feedback, ensuring any remaining errors are corrected before the actual exam.
  • Tool checklist — compass (holds width), sharp pencil, straight-edge, protractor; test before exam day
  • Practice target — minimum 5 repetitions per construction type, timed for exam speed
  • Conceptual understanding — memorize steps and reasoning; be ready to explain why each construction works
  • Show your work — never erase construction arcs; they earn method marks even if final figure is imperfect
  • Solve all NCERT exercises — 8.1 to 8.4, plus additional problems from reference books
  • Timed mock test — one week before exam, cover all construction types, get AI feedback on CBSETUTOR.ai

Frequently asked questions

Why must the compass be opened to more than half the segment length when constructing a perpendicular bisector in CBSE Class 6 Mathematics Chapter 8?+
If the compass width is less than half the segment length, the arcs drawn from both endpoints will not intersect on both sides of the segment. The intersection points P and Q are needed to draw the perpendicular bisector line. Setting the compass to more than half (ideally about three-quarters) ensures the arcs cross above and below, providing two clear points through which the bisector can be drawn.
Can I use a ruler to measure side lengths when constructing a triangle in CBSE Class 6 Mathematics Chapter 8 Playing with Constructions?+
You may use a ruler to draw the base segment (for example, AB = 5 cm) if the question provides a numerical length. However, for the remaining sides, you must use the compass to transfer the given lengths by setting the compass width to the required distance and drawing arcs. This trains you to rely on geometric relationships rather than measurement, which is the essence of construction in CBSE geometry.
What happens if I accidentally change the compass width while constructing a perpendicular bisector?+
If you change the compass width between drawing the arc from point A and the arc from point B, the arcs will have different radii. The intersection points P and Q will not be equidistant from both A and B, so the line PQ will not be the true perpendicular bisector. It may not pass through the midpoint or may not be perpendicular. Always keep the compass width fixed once set.
How do I verify that my perpendicular bisector construction in CBSE Class 6 Mathematics Chapter 8 is correct?+
After constructing the perpendicular bisector, measure the two segments on either side of the midpoint M (AM and MB) with a ruler. They should be equal. Also, use a protractor or set square to check that the bisector meets the original segment at a 90-degree angle. If both conditions are satisfied, your construction is correct.
Why is the SSS method the only way to construct a triangle when all three sides are given?+
The SSS method is based on the principle that if three side lengths are known and satisfy the triangle inequality (sum of any two sides greater than the third), exactly one triangle can be formed. The arcs drawn from two vertices intersect at a unique point (the third vertex), locking the triangle into one specific shape. No other triangle with those three side lengths is possible.
What should I do if the arcs I draw during triangle construction are too faint to see?+
Use a sharp pencil with enough pressure to leave a visible mark. If your compass pencil is dull, sharpen it or replace the lead. Construction arcs must be clearly visible so you can accurately identify intersection points. In exams, examiners need to see the arcs to award method marks, so never draw them too lightly.
Is it possible to construct a triangle with sides 2 cm, 3 cm, and 6 cm in CBSE Class 6 Mathematics Chapter 8?+
No, this construction is impossible because the sides violate the triangle inequality. The sum of the two shorter sides (2 + 3 = 5 cm) is not greater than the longest side (6 cm). In geometry, a triangle can only be formed if the sum of any two sides is strictly greater than the third side. Always check this condition before attempting a construction.
How many marks are typically awarded for construction questions in CBSE Class 6 Mathematics exams?+
Construction questions in CBSE Class 6 Mathematics exams usually carry 2–5 marks depending on complexity. Simple constructions like copying a line segment or drawing a circle are worth 2–3 marks, while perpendicular bisectors and triangle constructions (SSS, SAS) are worth 4–5 marks. Marks are awarded for correct method (visible arcs, labeled points) and accurate final figure.
Can I erase the construction arcs after completing the figure to make it look neater?+
No, never erase construction arcs. In CBSE exams, these arcs are evidence of your method. Even if your final figure is slightly inaccurate, you will earn partial marks if the arcs and steps are visible. Erasing arcs removes proof of your work and can result in lost marks.
Why is Playing with Constructions important for higher classes in CBSE?+
CBSE Class 6 Mathematics Chapter 8 Playing with Constructions lays the foundation for all geometry constructions in Classes 7–10. In Class 9 and 10 CBSE board exams, construction questions carry 6–8 marks and include constructing triangles, quadrilaterals, tangents to circles, and angle bisectors. Mastering compass-and-straight-edge techniques in Class 6 ensures students are prepared for these higher-level constructions.
What is the difference between SAS and SSA triangle construction?+
In SAS (Side-Angle-Side) construction, the angle is between the two given sides, which uniquely determines the triangle. In SSA (Side-Side-Angle), the angle is not between the two sides. SSA does not always produce a unique triangle; depending on the measurements, it may produce zero, one, or two different triangles. CBSE Class 6 Mathematics Chapter 8 focuses on SAS because it guarantees a unique construction.
How can CBSETUTOR.ai help if I keep making mistakes in constructions during practice?+
CBSETUTOR.ai allows you to upload a photo of your construction, and the AI analyzes it to identify specific errors such as incorrect compass width, arcs not intersecting, or mislabeled points. It then provides step-by-step corrective guidance so you can understand exactly what went wrong and how to fix it. This immediate, personalized feedback is not available in textbooks or video tutorials and accelerates learning, especially for hands-on skills like constructions in CBSE Class 6 Mathematics Chapter 8 Playing with Constructions.

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