Classifying quadrilaterals

In this lesson, we will learn:

• A quadrilateral is a polygon with 4 sides
• We can look at the properties of a quadrilateral (pairs of parallel sides, pairs of congruent sides, types of angles) to classify into 6 different types
• The special types of quadrilaterals are: rectangle, square, parallelogram, rhombus, trapezoid, and kite

Notes:

• A quadrilateral is a 2D shape with 4 straight sides (a 4-sided polygon)
• A quadrilateral also has 4 vertices (corners)
• Each corner contains an angle; the total angle sum in any quadrilateral is 360°


• There are special quadrilaterals with specific definitions and names
• There will be 6 types of quadrilaterals in this lesson: Rectangle, Square, Parallelogram, Rhombus, Trapezoid, and Kite
• A quadrilateral can fit the definition of more than one of these special types


• Rectangles and squares:
• Quadrilaterals with 4 right angles (all angles are 90° )
• A rectangle has 2 pairs of opposite and equal sides (congruent)
• A square is a special type of rectangle where all 4 sides are equal (congruent)
• All squares are rectangles, but not all rectangles are squares
• Rectangles and squares can also be considered as parallelograms, just with right angles


• Parallelograms and rhombuses:
• Quadrilaterals with 2 pairs of parallel sides and 2 pairs of opposite equal angles
• A parallelogram has 2 pairs of congruent sides (equal length)
• A rhombus has all 4 sides congruent (all 4 sides equal length)
• All rhombuses are parallelograms; not all parallelograms are rhombuses


• Trapezoids:
• Quadrilaterals with only 1 pair of parallel sides


• Kites:
• Quadrilaterals with 2 adjacent congruent sides (no parallel sides)
• There is 1 pair of opposite equal angles across the line of symmetry


• Summary of quadrilateral types and properties (sides and angles):