In parallelogram ABCD, the diagonals AC and BD meet at point O. Compare the lengths
| April 3, 2021 | education
In parallelogram ABCD, the diagonals AC and BD meet at point O. Compare the lengths of its sides AB and BC if the angle AOB is greater than the angle BOC.
Since the parallelogram has the diagonals, at the point of their intersection, they are divided in half, then in the triangles AOB and BOС, the side OB is common, and the side OA = OС as halves of the diagonals.
Then in the triangles AOB and BOС, by condition, the angle AOB is greater than the angle BOC, and since the larger side lies opposite the larger angle, then the AB side is larger than the BC side.
Answer: The AB side is larger than the BC side.
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