Given:
The objective is to prove that each pair of consecutive angles of a parallelogram are supplementary angles.
Explanation:
Consider a parallelogram ABCD with opposite parallel sides.
First consider the parallel sides AB || CD. Then, the sides AD and BC are transversal lines.
By the property of parallel lines, the sum of the angles on same side of a transversal is 180°.
[tex]\begin{gathered} \angle A+\angle D=180\degree\text{ . . . . (1)} \\ \angle B+\angle C=180\degree\text{ . . . . (2)} \end{gathered}[/tex]Now, consider the parallel sides as AD || BC. Then, the sides AB and CD are transversal lines.
By the property of parallel lines, the sum of the angles on same side of a transversal is 180°.
[tex]\begin{gathered} \angle A+\angle B=180\degree\text{ . . . . . (3)} \\ \angle C+\angle D=180\degree\text{ . . . . . . .(4)} \end{gathered}[/tex]Thus, the sum of any two sides of a parallelogram will always be 180°.
Hence, it is proved that in a parallelogram each pair of consecutive angles are supplementary.
