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Classifying polygons

Topic Notes

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):
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