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Important Questions: CBSE Class 7 Mathematics Chapter 9 Constructions

Constructions is a purely practical chapter in CBSE Class 7 Mathematics where every mark depends on accuracy, clarity, and correct sequencing of compass-and-ruler steps. Unlike algebraic chapters, even a small error in arc positioning or missing construction line can cost you marks. This question bank mirrors the exact style and difficulty of CBSE board papers, grouping questions by marks and providing model solutions so you know precisely what examiners look for in your answer sheet.

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Key takeaways

✓Chapter 9 Constructions carries 4–6 marks in CBSE Class 7 final exams, usually as 1–2 construction problems requiring precise compass-and-ruler steps.
✓Triangle construction questions are based on four criteria: SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), and RHS (right angle, hypotenuse, side).
✓Parallel line construction using a transversal and corresponding angles or alternate angles is a recurring 2–3 mark question type.
✓Perpendicular construction at a point on a line or from an external point forms the basis of many geometry proofs in higher classes.
✓CBSE examiners award full marks only when rough sketch, construction steps with labels, and final measurement (if asked) are all clearly shown.
✓Common mistakes include not marking arcs clearly, wrong arc radius, skipping the rough figure, and erasing construction lines — all lead to mark deductions.
✓CBSETUTOR.ai offers 24×7 AI tutoring with photo-upload geometry solving at ₹999/month flat for Classes 6–12, with a 3-day free trial to practice constructions interactively.

Chapter Overview and Marks Weightage in CBSE Exam

Chapter 9 Constructions introduces students to geometric drawing techniques that form the foundation for higher-class theorems and proofs. The NCERT syllabus for Class 7 Mathematics covers three main construction families: triangles (using SSS, SAS, ASA, and RHS criteria), parallel lines to a given line through a point, and perpendiculars to a line from a point on or off the line. In the CBSE annual exam, this chapter typically carries 4–6 marks, appearing as one 3-mark or one 5-mark construction problem, or occasionally split into a 2-mark and a 3-mark question. Since the chapter is purely practical, examiners award marks for neat labeling, visible construction arcs, correct sequence, and final accuracy. Students who lose marks here often do so not because they lack knowledge but because they skip the rough sketch, erase construction arcs, or mislabel vertices.

Expected weightage: 4–6 marks out of 80 (internal exams may vary to 8–10 marks if combined with Chapter 10 Visualising Solid Shapes)
Question pattern: 1 construction problem of 3 or 5 marks; occasionally 1 MCQ on construction steps (1 mark)
Marking scheme: 1 mark for rough sketch, 2–3 marks for correct construction steps with visible arcs, 1 mark for labeling and final statement
Time allocation: Spend 4–6 minutes on a 3-mark construction; 8–10 minutes on a 5-mark triangle construction
Tools allowed: Compass, ruler, protractor, and pencil — CBSE does not permit use of set squares for angle construction unless specified

1-Mark Questions (MCQ / Very Short Answer)

One-mark questions on Constructions test basic conceptual clarity and recognition of construction criteria. CBSE occasionally includes 1-mark MCQs asking which criterion applies to a given set of data or which step is incorrect in a construction sequence. These questions are quick scorers if you have memorised the four triangle construction criteria and the basic steps for parallel and perpendicular lines. Below are five representative 1-mark questions with concise answers.

Q1. Which criterion is used to construct a triangle when two sides and the included angle are given? — Answer: SAS (Side-Angle-Side) criterion.
Q2. In constructing a triangle with sides 5 cm, 6 cm, and 7 cm, which criterion applies? — Answer: SSS (Side-Side-Side) criterion.
Q3. True or False: A triangle can be constructed if two angles and a non-included side are given. — Answer: True (using ASA by calculating the third angle).
Q4. What is the first step in constructing a perpendicular to a line at a point on it? — Answer: Draw two arcs of equal radius on either side of the point on the line.
Q5. To construct a line parallel to a given line at distance 3 cm, you draw a perpendicular and mark a point at 3 cm, then draw a line through it. This method uses which property? — Answer: Equidistant property of parallel lines (or alternate interior angles if using transversal method).

2-Mark Questions (Short Answer)

Two-mark questions ask students to describe construction steps in words or perform a simple construction like drawing a perpendicular or identifying the correct criterion. CBSE examiners give 1 mark for correct identification and 1 mark for logical reasoning or partial construction steps. Clarity and use of correct geometric terms (arc, perpendicular bisector, transversal) are essential. Below are three typical 2-mark questions with model answers.

Q6. State the steps to construct a perpendicular to a line PQ at point M on it. — Answer: (i) With M as centre, draw arcs of equal radius cutting PQ at A and B. (ii) With A and B as centres and radius greater than AM, draw arcs intersecting at point N above PQ. (iii) Join MN; MN is perpendicular to PQ.
Q7. Can you construct a triangle with sides 3 cm, 4 cm, and 8 cm? Justify. — Answer: No. The sum of any two sides must be greater than the third side. Here 3 + 4 = 7 cm, which is less than 8 cm, violating the triangle inequality. Hence construction is not possible.
Q8. Which criterion would you use to construct a triangle ABC where AB = 5 cm, ∠A = 60°, and AC = 6 cm? Write the criterion name. — Answer: SAS criterion, because two sides (AB and AC) and the included angle (∠A) are given.
Q9. Draw a rough sketch of a triangle with a right angle at B, hypotenuse AC = 7 cm, and side AB = 4 cm. Which construction criterion applies? — Answer: Rough sketch shows right angle at B, AC as hypotenuse. Criterion is RHS (Right angle-Hypotenuse-Side).

3-Mark Questions (Construction with Steps)

Three-mark construction questions require a complete construction with rough sketch, labeled steps, and visible arcs. CBSE awards 1 mark for the rough figure, 1.5 marks for correct construction sequence with arcs, and 0.5 mark for final labeling and statement. Students must write steps in imperative sentences (Draw, Mark, Join) and retain all construction arcs in the final diagram. Below are four representative 3-mark questions with step-by-step model solutions.

5-Mark Questions and Case-Based Problems

Five-mark questions involve multi-step triangle constructions with additional tasks such as measuring angles or sides, or constructing altitudes and medians on the same triangle. CBSE introduced case-based questions from 2021 onwards; a typical case-based problem gives a real-world scenario (e.g. designing a triangular garden plot) followed by 2–3 sub-questions totaling 5 marks. The first sub-question often asks for the construction itself (3 marks), and remaining sub-questions test measurement or properties (1 mark each). Accuracy in measurement and neatness in construction lines are critical because examiners cross-check actual lengths and angles. Below are three representative 5-mark questions with detailed solutions.

How CBSE Frames Questions from This Chapter

CBSE question setters follow a predictable pattern for Constructions, leveraging the four triangle criteria and the two perpendicular/parallel line constructions as building blocks. Typically, the Class 7 annual paper includes exactly one construction question in Section B (3 marks) or Section C (5 marks). From 2018–2024 CBSE sample papers and board sets, roughly 60% of construction questions were SSS or SAS triangles, 20% were RHS triangles, 10% were ASA triangles, and 10% tested parallel or perpendicular line construction. The examiners vary the presentation: sometimes they give a word problem ('A ladder 5 m long leans against a wall…construct the triangle'), sometimes pure geometric data, and occasionally a diagram with missing labels that students must construct and complete. Five-mark questions almost always have a measurement sub-part to test whether the student's construction is accurate. Marks are deducted for invisible or erased construction arcs, unlabeled vertices, missing rough sketch, and incorrect final measurements beyond ±2 mm tolerance.

Standard phrasing: 'Construct a triangle ABC where…', 'Draw a line parallel to…', 'Construct the perpendicular from point P to line l'
Measurement sub-questions: 'Measure and write the length of…', 'Verify your construction by measuring angle…' — tolerance is ±2 mm or ±2°
Justification sub-questions: 'State which criterion you used', 'Is it possible to construct this triangle? Give reason'
Combination tasks (5 marks): Construct triangle + draw altitude + measure altitude length, or construct triangle + draw angle bisector + verify angle
Case-based scenarios (introduced 2021): Real-world context (park, roof truss, signal tower) followed by 2–3 construction or measurement sub-questions totaling 4–5 marks
Common data sets: Sides in the range 3–8 cm, angles 30°, 45°, 60°, 90°, 120° (easy to construct with compass and protractor)

Common Mistakes Students Make and How to Avoid Them

Even students who understand the theory lose marks in Constructions due to procedural errors. The single biggest mistake is erasing construction arcs after drawing the final figure — CBSE marking schemes explicitly state that arcs must be visible to award full method marks. Another frequent error is skipping the rough sketch; examiners allocate 0.5–1 mark for it, and its absence signals lack of planning. Incorrect arc radius is common in SSS and SAS constructions: students sometimes measure the arc radius from the wrong vertex or use the protractor incorrectly for angles. Mislabeling vertices (writing P, Q, R when the question asks for A, B, C) costs 0.5 mark. In parallel line construction, students often draw the transversal but forget to verify equal corresponding or alternate angles. During exams, time pressure leads to hasty protractor readings (reading the wrong scale) and ruler misalignment. Practising 15–20 constructions before the exam and using a sharp HB pencil with a good-quality compass dramatically improves accuracy and speed.

Erasing arcs: Never erase construction arcs — they are proof of your method. Keep them light but visible.
No rough sketch: Always draw a small rough figure in the margin and label it; this earns 0.5–1 mark and helps you visualise the final shape.
Wrong arc radius: Double-check which vertex is the centre and which measurement is the radius before drawing each arc.
Protractor misreading: Use the correct scale (inner or outer) and align the baseline exactly with the line segment; common error is reading 120° instead of 60°.
Unlabeled or mislabeled points: Match your labels exactly to the question; write labels clearly near each vertex.
Joining wrong points: After arcs intersect, double-check which points to join — especially in perpendicular constructions from external points.
Thick or multiple lines: Use a sharp pencil and draw each line once; overwriting or thick lines make arc intersections unclear to the examiner.
Skipping the 'required' statement: End with 'Hence triangle ABC is the required triangle' or 'PQ is the required parallel line' — shows completeness.

Criteria-Wise Question Breakdown: SSS, SAS, ASA, RHS

Understanding when to apply each criterion is half the battle. SSS (Side-Side-Side) is used when all three side lengths are given; you draw one side as the base and use two arcs to locate the third vertex. SAS (Side-Angle-Side) applies when two sides and the included angle are known; draw one side, construct the angle at one end, mark the second side along the angle ray, then join. ASA (Angle-Side-Angle) is less common in Class 7 but appears when two angles and the included side are given; construct both angles at the ends of the given side and extend the rays until they meet. RHS (Right angle-Hypotenuse-Side) is specific to right triangles: draw the side adjacent to the right angle, construct a 90° perpendicular, then use the hypotenuse length as an arc radius to locate the third vertex. CBSE examiners test recognition by giving data sets and asking 'Which criterion applies?' or by giving a criterion and asking students to construct a matching triangle. Knowing these four patterns by heart ensures you never waste time wondering where to start.

SSS: All three sides given — Example: PQ = 5 cm, QR = 6 cm, PR = 7 cm. Draw base QR, arcs from Q and R intersect at P.
SAS: Two sides and included angle — Example: AB = 4 cm, ∠A = 50°, AC = 5 cm. Draw AB, construct 50° at A, mark C at 5 cm, join BC.
ASA: Two angles and included side — Example: ∠B = 60°, BC = 6 cm, ∠C = 45°. Draw BC, construct 60° at B and 45° at C, rays meet at A. (Third angle = 75° by angle sum property.)
RHS: Right angle, hypotenuse, one side — Example: Right angle at Q, hypotenuse PR = 10 cm, side PQ = 6 cm. Draw PQ = 6 cm, perpendicular at Q, arc from P radius 10 cm cuts perpendicular at R.
Quick recognition tip: If three sides → SSS; two sides + angle between them → SAS; two angles + side between → ASA; right angle + hypotenuse + other side → RHS.
CBSE typically gives SSS and SAS most often (combined ~70% of questions), RHS next (~20%), ASA least (~10%).

Parallel and Perpendicular Line Constructions

Constructing parallel and perpendicular lines using only compass and ruler is a fundamental skill tested both independently and as part of larger geometry problems. For a perpendicular to a line at a point on the line, the standard method is to draw equal arcs on both sides of the point, then from those arc-intersections draw arcs above (or below) the line that intersect; joining that intersection to the original point gives the perpendicular. For a perpendicular from an external point, draw an arc from the external point cutting the line at two points, then use those two points as centres to draw intersecting arcs on the opposite side; join the external point to that intersection. For parallel lines, the most reliable method is to draw a perpendicular to the given line, mark off the desired distance along the perpendicular, then construct another perpendicular at that point — the two perpendiculars to the same transversal are parallel. Alternatively, use the property of alternate interior angles: draw a transversal, copy the angle, and extend. CBSE questions often ask students to construct a parallel line 'at a distance of 3 cm' or 'through point P', testing both methods.

Perpendicular at a point M on line l: Equal arcs left-right from M on l → arcs above from those points intersect at N → join MN.
Perpendicular from external point P to line l: Arc from P cuts l at A, B → arcs from A, B below l intersect at Q → join PQ (PQ ⊥ l).
Parallel line at distance d: Draw perpendicular to given line → mark point at distance d on perpendicular → draw another perpendicular through that point.
Parallel line through point P (alternate angle method): Draw any transversal through P cutting given line at Q → measure ∠ at Q → copy that angle at P on same side → extend to get parallel line.
Common exam question: 'Draw a line parallel to AB passing through point P which is 4 cm from AB' — use perpendicular method.
Mark allocation: 2 marks for perpendicular construction, 3 marks for parallel line construction with visible arcs and labels.

Step-by-Step Guide: Constructing an RHS Triangle

RHS triangle construction is a favourite of CBSE examiners because it combines perpendicular construction with arc intersection. The data will specify a right angle at one vertex, the hypotenuse, and one other side. Start by drawing the given side (not the hypotenuse) as a horizontal base. At one end of this base, construct a 90° perpendicular — you can do this with a protractor or by the compass method (equal arcs method). Now take the hypotenuse length as radius, place the compass point at the other end of the base, and draw an arc that cuts the perpendicular ray. That intersection point is the third vertex; join it to complete the triangle. Many students mistakenly try to draw the hypotenuse first, which makes locating the right angle difficult. Always start with the side adjacent to the right angle. After construction, you can verify by measuring the hypotenuse or using Pythagoras' theorem mentally to check if your drawing is accurate.

Step 1: Identify which side is adjacent to the right angle (not the hypotenuse). Draw that side, say PQ = 6 cm, as base.
Step 2: At Q, construct a perpendicular QX using compass: equal arcs from Q on PQ, then arcs above intersecting, join intersection to Q.
Step 3: Given hypotenuse PR = 10 cm. With P as centre and radius 10 cm, draw an arc cutting QX at R.
Step 4: Join PR. Triangle PQR is the required RHS triangle with right angle at Q, hypotenuse PR = 10 cm, side PQ = 6 cm.
Step 5: Verification: Measure QR; it should equal √(PR² − PQ²) = √(100 − 36) = √64 = 8 cm.
Common mistake: Students sometimes draw the hypotenuse first or use protractor carelessly, getting 89° or 91° instead of exactly 90°. Use compass method for precision.

Practice Strategy and Time Management for Constructions

Constructions is one chapter where practice directly translates to marks. Aim to complete at least 15–18 different construction problems — 3–4 from each criterion (SSS, SAS, ASA, RHS) plus 3–4 parallel and perpendicular line constructions — before the exam. Use NCERT Exercise 9.1 through 9.5, NCERT Exemplar, and your school question bank. Time yourself: spend no more than 4 minutes on a 2-mark construction, 6 minutes on a 3-mark, and 10 minutes on a 5-mark. During the exam, read the question carefully to identify the criterion or construction type before picking up the compass. Draw the rough sketch first in the margin; this 30-second investment saves minutes of confusion later. Keep your compass tight (loose compass leads to inaccurate arcs), sharpen your pencil before the exam, and carry a good eraser but use it sparingly. If you make an error, draw a single light line through the mistake and redo neatly beside it rather than heavy scribbling. Finally, always end with a concluding statement and double-check that all vertices are labeled as per the question. CBSETUTOR.ai's AI tutor can review photos of your construction attempts and provide instant feedback on arc placement, labeling, and method — a powerful way to self-correct between practice sessions.

Daily practice: 2 constructions per day for 10 days before exam — mix criteria and difficulty levels.
Use quality tools: Compass with tight joint, 15 cm ruler with clear mm markings, 180° protractor, sharp HB pencil.
Rough sketch habit: Spend 20–30 seconds on a labeled rough figure before every construction, even in practice.
Visibility of arcs: Draw arcs lightly but clearly; examiners should see arc intersections without straining.
Labeling discipline: Write vertex labels immediately after locating each point; do not leave labeling for the end.
Time benchmarks: 2-mark → 4 min, 3-mark → 6 min, 5-mark → 10 min. Practice with a timer to build speed.
Self-review: After each construction, verify by measuring all sides and angles; compare with expected values (tolerance ±2 mm or ±2°).
CBSETUTOR.ai advantage: Upload a photo of your construction; the AI tutor will check arc positions, correct sequence, and suggest improvements — available 24×7 at ₹999/month for all subjects and classes, 3-day free trial included.

Frequently asked questions

How many marks does Chapter 9 Constructions carry in CBSE Class 7 final exam?+

Constructions typically carries 4–6 marks in the CBSE Class 7 Mathematics annual exam, usually as one 3-mark or one 5-mark construction problem. Internal school exams may allocate up to 8–10 marks if combined with related geometry chapters.

Which triangle construction criterion is most frequently asked in CBSE Class 7 exams?+

SSS (Side-Side-Side) and SAS (Side-Angle-Side) are the most common, appearing in roughly 70% of CBSE construction questions. RHS (Right angle-Hypotenuse-Side) accounts for about 20%, and ASA (Angle-Side-Angle) about 10% of past-year questions.

Do I lose marks if I erase the construction arcs in my final diagram?+

Yes. CBSE marking schemes require visible construction arcs to award full method marks. Erasing arcs can result in loss of 1–2 marks even if the final triangle is correct, because the examiner cannot verify your construction steps.

Is it compulsory to draw a rough sketch before the actual construction?+

While not always explicitly mentioned, CBSE examiners allocate 0.5–1 mark for a rough sketch. Drawing it also helps you plan vertex positions and avoid errors, so it is highly recommended and often expected in 3-mark and 5-mark questions.

Can I use a set square to construct right angles instead of a compass?+

CBSE exam instructions typically allow compass, ruler, and protractor. Set squares are permitted only if the question explicitly states so. For maximum marks and to demonstrate method, use the compass-based perpendicular construction technique taught in NCERT.

How do I construct a triangle when two angles and one side are given (ASA)?+

Draw the given side as base. At each endpoint, use a protractor to construct the given angles. Extend the two angle rays until they intersect; that intersection is the third vertex. Join to complete the triangle. Ensure angle measurement is accurate to within ±2°.

What is the correct method to construct a line parallel to a given line at 3 cm distance?+

Draw a perpendicular to the given line at any point. Measure 3 cm along the perpendicular and mark a point. At that point, construct another perpendicular to the first perpendicular; this new line will be parallel to the original line and exactly 3 cm away.

Why does my RHS triangle construction sometimes fail to close properly?+

Common causes: (i) drawing the hypotenuse as the base instead of the side adjacent to the right angle, (ii) perpendicular not exactly 90° (use compass method, not protractor alone), (iii) wrong arc radius (should be hypotenuse length). Always start with the non-hypotenuse side and construct the right angle first.

How much measurement error is acceptable in CBSE Class 7 construction answers?+

CBSE allows a tolerance of ±2 mm for length measurements and ±2° for angle measurements. Beyond this, marks may be deducted. Ensure your compass is tight and your ruler and protractor are aligned accurately to stay within tolerance.

Can CBSETUTOR.ai help me improve my construction accuracy and speed?+

Yes. CBSETUTOR.ai's AI tutor accepts photo uploads of your construction diagrams and provides instant feedback on arc placement, correct sequencing, labeling, and common errors. It is available 24×7 for Classes 6–12 at a flat ₹999/month with a 3-day free trial, making it ideal for regular construction practice and self-assessment.

Related resources

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