Discovering properties of angles of parallelograms

Consider the parallelogram below. We mark the bottom-left angle with a and the bottom-right angle with b to denote their measures as shown in Figure 1.

Figure 1

We create another parallelogram with same size and the shame shape, but of different color. We place the two parallelograms side by side as shown in Figure 2. The angles a and b is a linear pair; therefore, (1) a  + b = 180˚

Figure 2

We create two more parallelograms and place them as shown in Figure 3 to form a bigger parallelogram. Angle a in the red parallelogram and the adjacent angle in the blue parallelogram is also a linear pair; therefore, the upper-left angle in the blue parallelogram also equals b (see Figure 4).  In effect, the the upper-right angle in the yellow parallelogram also equals the measure of angle a. » Read more