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source: ncert
topic: geometry
class_level: class_8
chapter: ch3
difficulty: beginner
---
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°). |