Question 171
Let $ABCD$ be a convex quadrilateral such that
$$
|AB| + |CD| = \sqrt{2} \cdot |AC| \quad \text{and} \quad |BC| + |DA| = \sqrt{2} \cdot |BD|.
$$
Prove that $ABCD$ is a parallelogram.
$$
|AB| + |CD| = \sqrt{2} \cdot |AC| \quad \text{and} \quad |BC| + |DA| = \sqrt{2} \cdot |BD|.
$$
Prove that $ABCD$ is a parallelogram.