Learning Objectives
- Classify polygons based on their sides and angles
- Understand the angle sum property of polygons
- Learn properties of different types of quadrilaterals
- Identify and differentiate parallelograms, rhombus, rectangle, square, kite, and trapezium
Key Concepts
Polygons
A polygon is a simple closed curve made up of line segments. A polygon with n sides has an angle sum of (n - 2) × 180°. The sum of exterior angles of any convex polygon is always 360°.
- Triangle: 3 sides, angle sum = 180°
- Quadrilateral: 4 sides, angle sum = 360°
- Pentagon: 5 sides, angle sum = 540°
- Hexagon: 6 sides, angle sum = 720°
Types of Quadrilaterals
Trapezium: A quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases and the non-parallel sides are called legs.
Parallelogram: A quadrilateral with both pairs of opposite sides parallel. Properties: opposite sides are equal, opposite angles are equal, diagonals bisect each other, adjacent angles are supplementary (sum = 180°).
Rhombus: A parallelogram with all four sides equal. Additional property: diagonals bisect each other at right angles (90°).
Rectangle: A parallelogram with all angles equal to 90°. Additional property: diagonals are equal in length.
Square: A parallelogram that is both a rhombus and a rectangle. All sides equal, all angles 90°, diagonals are equal and bisect at right angles.
Kite: A quadrilateral with two pairs of adjacent sides that are equal. Diagonals are perpendicular; one diagonal bisects the other.
Hierarchy of Quadrilaterals
Every square is a rectangle, every rectangle is a parallelogram, every parallelogram is a trapezium. Every square is a rhombus, every rhombus is a parallelogram.
Summary
Quadrilaterals are four-sided polygons with an angle sum of 360°. They include trapezium, parallelogram, rhombus, rectangle, square, and kite, each with distinct properties related to sides, angles, and diagonals. Understanding the hierarchy helps in identifying relationships between different quadrilaterals.
Important Terms
- Polygon: A closed figure made of line segments
- Convex Polygon: All interior angles are less than 180°
- Concave Polygon: At least one interior angle is greater than 180°
- Diagonal: A line segment connecting two non-adjacent vertices
- Supplementary Angles: Two angles whose sum is 180°
- Bisect: To divide into two equal parts
Quick Revision
- Angle sum of polygon = (n - 2) × 180°
- Sum of exterior angles = 360° for any convex polygon
- Parallelogram: opposite sides parallel and equal, diagonals bisect each other
- Rhombus: all sides equal, diagonals bisect at 90°
- Rectangle: all angles 90°, diagonals are equal
- Square = Rectangle + Rhombus (all sides equal, all angles 90°)