Question

(04.01 lc)
how could you use coordinate geometry to prove that $overline{bc}congoverline{ad}$?
prove the slopes are the same.
prove the slopes are opposite reciprocals.
prove the lengths are the same.
prove the midpoints are the same.

Explanation:

Step1: Recall the meaning of congruent segments

Two line - segments $\overline{BC}$ and $\overline{AD}$ are congruent ($\overline{BC}\cong\overline{AD}$) if and only if their lengths are equal. In coordinate geometry, the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ can be used to find the lengths of the line - segments. If the lengths calculated for $\overline{BC}$ and $\overline{AD}$ are the same, then $\overline{BC}\cong\overline{AD}$.

Step2: Analyze other options

Proving slopes are the same shows parallel lines, not congruent segments. Proving slopes are opposite reciprocals shows perpendicular lines. Proving mid - points are the same does not imply the segments are congruent.

Answer:

C. Prove the lengths are the same.