source: ncert
topic: geometry
class_level: class_8
chapter: ch4
difficulty: beginner
Class 8 | Ch4: Practical Geometry (Quadrilaterals) A quadrilateral has 4 sides, 4 angles, 2 diagonals = 10 measurements total. Minimum 5 measurements needed to uniquely construct a quadrilateral. CONSTRUCTION CASES: Case 1 — Four sides and one diagonal (SSS triangles method): Draw diagonal first, construct both triangles on either side. Case 2 — Two diagonals and three sides: Draw one diagonal, use given measurements to find vertices. Case 3 — Two adjacent sides and three angles: Use angles to set directions, mark lengths. Case 4 — Three sides and two included angles: Draw one side, use angles at both ends. Case 5 — Special quadrilaterals (rhombus, rectangle, square): Use their special properties to simplify construction. CONSTRUCTING QUADRILATERAL ABCD (4 sides + 1 diagonal): Given: AB=4cm, BC=3.5cm, CD=4.5cm, DA=3cm, AC=5cm. Step 1: Draw AC=5cm (diagonal). Step 2: From A, draw arc radius 4cm. From C, draw arc radius 3.5cm. Intersection=B. Step 3: From A, draw arc radius 3cm. From C, draw arc radius 4.5cm. Intersection=D. Step 4: Join all vertices. ABCD is the required quadrilateral. RHOMBUS CONSTRUCTION: Both diagonals given (they bisect at right angles at midpoint). RECTANGLE CONSTRUCTION: One side and one diagonal (use Pythagoras to find other side). COMMON MISTAKES: Check if given measurements form a valid quadrilateral before constructing. In rhombus construction, diagonals bisect each other at 90°, not just bisect.