$\"\"$

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Since $\"\"$ is the midsegment of $\"\"$ , D and E are the midpoints of $\"\"$ and $\"\"$ .

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Let the midpoint of $\"\"$ is D, and $\"\"$ is E.

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Use the midpoint formula to determine D and E.

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The midpoint formula is $\"\"$ .

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Midpoint D = $\"\"$ (Substitute $\"\"$ )

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Midpoint D = $\"\"$ (Simplify)

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Midpoint E = $\"\"$ (Substitute $\"\"$ )

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Midpoint E = $\"\"$ (Simplify)

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D = $\"\"$ and E = $\"\"$ . $\"\"$

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Use distance formula to find DE and BC.

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The distance formula is $\"\"$ .

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Find DE.

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Simplify)

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Find BC.

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Simplify) $\"\"$

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Verify that $\"\"$ .

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$\"\"$ (Substitute DE = 7 and BC = 14)

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$\"\"$ (Simplify)

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The solution is true. $\"\"$

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DE = 7 and BC = 14 ; $\"\"$ .