Constructions

• How to construct quadrilaterals when given sides, diagonals, or angles — using ruler and compass only.
• Step-by-step construction of special quadrilaterals: parallelogram, rectangle, rhombus, square.
• How to construct a perpendicular bisector, angle bisector, and 60° angle.
• Why accurate construction matters in design, engineering drawings, and CBSE board exams.

1. Tools — Ruler (straight edge), compass, protractor (for checking only in some steps). Constructions use logical steps, not measurement guessing.

2. Perpendicular bisector of a segment — Every point on it is equidistant from the endpoints. Used to locate mid-points and right angles.

3. Constructing a quadrilateral (SSSS) — Given four sides and one diagonal: draw base, arcs for remaining sides, join vertices.

4. Parallelogram construction — Draw base AB, construct angle at A, mark AD = given side, complete with parallel sides (alternate angles / parallel line construction).

5. Rhombus — All sides equal: construct two arcs of same radius from adjacent vertices, or use diagonals that bisect at right angles.

6. Square — Rectangle with equal sides, or rhombus with 90° angles. Often built from two perpendicular equal segments at the centre.

7. Where it shows up — Technical drawing, architecture blueprints, designing logos with symmetry, and verifying geometric theorems on paper.

Construct a quadrilateral ABCD with AB = 5 cm, BC = 4 cm, CD = 3 cm, DA = 4.5 cm, and AC = 6 cm.

Step 1 — Draw AB = 5 cm
Step 2 — With A as centre, radius 4.5 cm, draw an arc
Step 3 — With B as centre, radius 4 cm, draw an arc; mark C
Step 4 — Join AC and check AC = 6 cm (adjust C if needed using compass)
Step 5 — With A centre 4.5 cm and C centre 3 cm, arcs intersect at D
Step 6 — Join CD and DA
Answer: Quadrilateral ABCD constructed

Application: A carpenter lays out a rectangular frame by constructing right angles at corners using perpendicular bisectors — ensuring the floor tile grid is perfectly square.

• Using approximate measurements instead of compass arcs for equal lengths.
• Not labelling vertices in order (ABCD should go around the shape).
• Forgetting to draw the diagonal first when SSSS data includes it.
• Skipping the step that verifies a required angle (e.g. 90° for a rectangle).

• List the data needed to construct a unique quadrilateral (minimum five measurements).
• How do you construct a 60° angle at a point?
• What is the first step in constructing a rhombus of side 4 cm?
• Why must diagonals of a constructed square bisect at 90°?

Open the Practice tab for graded questions on Constructions.