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how could you use coordinate geometry to prove that $overline{bc} \cong \overline{ad}$?
prove the slopes are the same.
prove the slopes are opposite reciprocals.
prove the lengths are the same.
prove the midpoints are the same
The notation $\overline{BC} \cong \overline{AD}$ means the two line segments are congruent, which in coordinate geometry means they have equal lengths. Proving slopes are the same shows lines are parallel, opposite reciprocals shows perpendicularity, and same midpoints shows segments bisect each other—none of these relate to congruence of the segments themselves.
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Prove the lengths are the same.