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