| --- |
| source: ncert |
| topic: geometry |
| class_level: class_8 |
| chapter: ch3 |
| difficulty: beginner |
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| |
| Class 8 | Ch3: Understanding Quadrilaterals |
| ANGLE SUM PROPERTY: |
| Sum of interior angles of polygon with n sides = (n-2)×180°. |
| Triangle(n=3): (3-2)×180=180°. |
| Quadrilateral(n=4): (4-2)×180=360°. |
| Pentagon(n=5): 540°. Hexagon(n=6): 720°. |
| Sum of exterior angles of ANY convex polygon = 360°. |
| TYPES OF QUADRILATERALS AND PROPERTIES: |
| Trapezium: one pair of parallel sides. Area=(1/2)×(sum of parallel sides)×height. |
| Kite: two pairs of adjacent sides equal. One diagonal bisects the other at right angles. |
| Parallelogram: opposite sides parallel and equal, opposite angles equal, diagonals bisect each other. |
| Rectangle: parallelogram with all right angles, diagonals equal. |
| Rhombus: parallelogram with all sides equal, diagonals bisect at right angles. |
| Square: all sides equal, all angles 90°, diagonals equal and bisect at right angles. |
| HIERARCHY: Square → Rectangle → Parallelogram → Quadrilateral. |
| Square is special rhombus AND special rectangle. |
| SOLVED EXAMPLES: |
| Example 1: In parallelogram ABCD, angle A=75°. |
| Angle C=75° (opposite angles equal). Angle B=180-75=105° (co-interior=180°). Angle D=105°. |
| Example 2: Exterior angle of regular polygon=40°. How many sides? |
| Number of sides=360°/40°=9 sides. |
| Example 3: In kite ABCD, AB=AD=5cm, BC=DC=8cm. diagonal AC=6cm. Find BD. |
| Diagonals of kite are perpendicular. One diagonal bisects the other. |
| COMMON MISTAKES: |
| All rectangles are parallelograms but NOT all parallelograms are rectangles. |
| Rhombus diagonals bisect at 90° but are NOT equal. Rectangle diagonals are equal but NOT at 90°. |
| Sum of angles of quadrilateral=360° (not 180°). |
