Parallelograms & Related Quadrilaterals

General Properties of a Parallelogram:

• The opposite sides are parallel
• The opposite sides are equal
• The opposite angles are equal
• The diagonals bisectBisect means dividing into two equal parts. It means to divide a geometric figure such as a line, an angle or any other shape into two congruent parts (or two parts... More one another
• The formula for finding the sum of the measure of the interior angles is (n – 2) × 180º
• There are 4 sides in a parallelogram; therefore, the sum of the interior angles of a parallelogram is:
  • (4 – 2) × 180º
  • = 360 º

Types of Parallelogram:

1. Rhomboid:

This is a quadrilateral which has both pairs of opposite sides parallel.

A rhomboid is often referred to as a parallelogram.

Properties of a Rhomboid:

• The opposite sides are parallel
• The opposite sides are equal |AD| = |BC|, |AB| = |DC|
• The opposite angles are equal ∠A = ∠C, ∠D = ∠B
  • y₂ = y₁ , x₂ = x₁ (alternate angles)
  • ΔACB ≅ ΔACD (congruent triangles)
• The diagonals bisect one another
• Consecutive angles are supplementarySupplementary angles are two angles whose sum is 180 degrees. More (meaning they add up to 180º)

2. Rhombus:

Properties of a