Final answer:
To prove that ABCD is a parallelogram, we can use the fact that angles A and B and angles A and D are supplementary to show that opposite sides AB and CD and opposite sides AD and BC are parallel.
Step-by-step explanation:
To prove that ABCD is a parallelogram, we need to show that opposite sides are parallel. Given that angles A and B are supplementary (meaning they add up to 180 degrees) and angles A and D are supplementary, we can use this information to prove that opposite sides AB and CD are parallel, and opposite sides AD and BC are parallel.
Supplementary angles are angles that add up to 180 degrees. Since angles A and B are supplementary, we know that AB is a straight line. Similarly, since angles A and D are supplementary, AD is also a straight line. Since AB and CD are both straight lines and angles A and B are supplementary, we can conclude that AB and CD are parallel. Likewise, since angles A and D are supplementary and AD is a straight line, angles D and C also add up to 180 degrees and AD and BC are parallel.
Therefore, based on the given information, we have proven that ABCD is a parallelogram.