Trapezoids and Quadrilaterals

• Parallelogram


  A quadrilateral in which both pairs of the opposite sides are parallel
• Parallelogram


  • The opposite sides are congruent
  • Opposite angles are congruent
  • Two consecutive angles are supplementary
  • If an interior angle is a right angle, then all the interior angles are right angles
  • The diagonals bisect each other
  • The diagonals separate it into two congruent triangles
• Proving a quadrilateral is a parallelogram

  1. A quadrilateral is a parallelogram if both pairs of opposite sides are parallel
  2. A quadrilateral is a parallelogram if both pairs of opposite sides are congruent
  3. A quadrilateral is a parallelogram if both pairs of opposite angles are congruent
  4. A quadrilateral is a parallelogram is its diagonals bisect each other
  5. A quadrilateral is a parallelogram if one pair of sides is both parallel and congruent
• Kinds of parallelograms

  • Rectangle
  • Rhombus
  • Square
• Rectangle


  • A parallelogram with four right angles
  • Congruent diagonals
• Rhombus


  • A parallelogram with four congruent sides
  • Perpendicular diagonals that bisect each other
• Square


  • A rectangle with four congruent sides
  • All the properties of a parallelogram, rectangle, and rhombus
• Trapezoid


  A quadrilateral that has exactly one pair of legs called bases
• Isosceles trapezoid


  • The legs are congruent
  • The upper and lower base angles are congruent
• Median of a trapezoid


  The segment joined by the midpoints of its legs
• The median of a trapezoid is parallel to the bases, and its length is one-half the sum of the lengths of the bases
• Quilting pantograph


  A mechanical device that uses the concept of a parallelogram to accurately transfer mechanical motion from one place to the other
• Quadrilateral


  A polygon of four sides. The sum of the measures of the interior angles of a quadrilateral is 360