Question

a paragraph proof is written below for the following information. given: $overline{ab}$ with points $c$ and $d$ as shown. $overline{ac}congoverline{bd}$. prove: $overline{ad}congoverline{cb}$. it is given that $overline{ab}$ has points $c$ and $d$ as shown in the diagram. $overline{ac}congoverline{bd}$ is also given. this means that $ac = bd$ by the definition of congruence, and that $ac + cd=cd + db$ by the addition property of equality. the segment addition property gives $ac + cd = ad$ and $cd + db = cb$. therefore $overline{ad}congoverline{cb}$. choose the best statement about the proof. the proof is well written and all statements are justified. the statement $ac + cd = cd + db$ should be justified by the substitution property of equality. a statement should be made before $overline{ad}congoverline{cb}$, that says $ad = cb$ by the substitution property of equality, and the last statement needs definition of congruence as justification. the statement to be proved has not been proven and more information is needed.

Explanation:

The proof shows $AC = BD$ from congruence. Then uses segment - addition to get $AC + CD=AD$ and $CD + DB = CB$. But to conclude $\overline{AD}\cong\overline{CB}$, we first need to state $AD = CB$ using substitution property of equality and then use the definition of congruence (if two segments have equal lengths, they are congruent).

Answer:

A statement should be made before $\overline{AD}\cong\overline{CB}$, that says $AD = CB$ by the Substitution Property of Equality, and the last statement needs definition of congruence as justification.