| --- |
| 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. |
