Polygons and Quadrilaterals

Name: Sophia Breton

6.1 Polygons

  • Introduction to polygons:

    • Definition of a polygon: A closed figure formed by a finite number of line segments called sides.

    • Basic classifications of polygons based on the number of sides.

6.2 Quadrilaterals

  • General characteristics of quadrilaterals: Four-sided polygon.

  • Interior angles of a quadrilateral:

    • The sum of the interior angles can be computed using the formula:
      (n-2) imes 180 where $n$ is the number of sides (for quadrilaterals, $n=4$).

    • Therefore, for any quadrilateral:

      • Sum of interior angles = 360 degrees.

  • Exterior angles of polygons:

    • The sum of exterior angles of any polygon is always 360 degrees.

  • Regular polygons (equilateral and equiangular):

    • All sides and angles are congruent.

Examples of Quadrilaterals:

  • Trapezoids:

    • Characterized by having one pair of parallel sides.

    • Properties include:

    • Base angles are supplementary (sum = 180 degrees).

    • Legs can be congruent (isosceles trapezoid).

    • Diagonals may or may not be congruent depending on the type of trapezoid.

6.3 Kites

  • Definition of a kite in geometry:

    • A quadrilateral with two distinct pairs of adjacent sides that are equal in length.

  • Properties of kites:

    • Diagonals intersect at right angles.

    • The longer diagonal bisects the shorter diagonal.

    • One pair of opposite angles are equal (angles between unequal sides).

6.4 Parallelograms

  • Definition of a parallelogram:

    • A quadrilateral with opposite sides that are both parallel and equal in length.

  • Main properties:

    • Opposite angles are congruent.

    • Consecutive angles are supplementary (sum = 180 degrees).

    • Diagonals bisect each other (the point where they cross divides them into equal lengths).

6.5 Special Parallelograms

  • Types of special parallelograms:

    • Rectangle:

    • Is a parallelogram with four right angles.

    • Has congruent diagonals.

    • Rhombus:

    • Is a parallelogram with all four sides equal in length.

    • Diagonal lines are perpendicular to each other.

    • Diagonals bisect the angles of the rhombus.

    • Square:

    • Is a parallelogram that is both a rectangle and a rhombus.

    • Possesses all properties of a rectangle and a rhombus: four right angles, congruent sides, perpendicular diagonals, and diagonals bisecting angles.