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Chapter 5: 1 (page 166)
\(\iint_{\text{S}} {\text{F}} \times {\text{dS = 0}}\)
\[\iint_{\text{S}}{{\text{(}}\nabla{\text{f\times}}\nabla{\text{g)}}}\cdot{\text{dS}}\]
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Prove: If a segment whose endpoints lie on opposite sides of a parallelogram passes though the midpoint of a diagonal, that segment is bisected by the diagonal.
Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.
Theorem 5-5.
Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.
What values must x and y have to make the quadrilateral a parallelogram?
Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.
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