Shape and Space – Properties of a Parallelogram

Parallelogram 

. A 2D shape with opposite sides that are equal and parallel and opposite angles that are equal

. Line AB = line DC and they are parallel (never meet)

. Line AD = Line BC and they are parallel

. Angle A = Angle C (A + C = 180°)

. Angle B = Angle D (B + D = 180°)

. Therefore, angles in a parallelogram = 360°

. Alternate angles (y°) are equal can be found by drawing a Z onto the parallelogram 

. The alternate angles are the angles inside the Z

. The lines across the parallelogram, e.g A to C and B to D, are called diagonal lines

.  Both diagonal lines bisect each other at midpoint X

.  AX = XC and BX = XD

Example:

Q) Find the length DC and size of angle C

1. In a parallelogram opposite sides are equal in length – AB = 15cm, DC = 15cm
2. Interior angles in parallelogram are equal angle D = 70° and opposite angles are equal angle B = 70° 

. Angles in a parallelogram equal 360° → 360 – (70 + 70) = 240°, angle A + angle B = 220°

. Opposite angles are equal 220 ÷ 2 = 110°

A) 15cm and 110°