Question

Directions: For what values of X and Y must each figure be a parallelogram? Please explain the steps.

a) X = Y
b) X = -Y
c) X + Y = 180 degrees
d) X + Y = 360 degrees

Answer 1

a) The figure is a parallelogram when X = Y.

b) The figure is a parallelogram when X = -Y.

Step-by-step explanation:

a) In a parallelogram, opposite angles are equal. So, for figure a, X= Y ensures that opposite angles are congruent, making the figure a parallelogram.

b) Similarly, in figure b, opposite angles are equal. Therefore, X = -Y ensures the equality of opposite angles, satisfying the condition for a parallelogram.

c) For figure c, adjacent angles in a parallelogram add up to 180 degrees. Hence, X + Y = 180 degrees ensures that the figure is a parallelogram by satisfying the angle-sum property.

d) In figure d, adjacent angles in a parallelogram add up to 360 degrees. Therefore, X + Y = 360 degrees ensures that the figure is a parallelogram by meeting the angle-sum criterion.