Question

proof in the figure, point b is the mid - point of $overline{ac}$ and point c is the mid - point of $overline{bd}$. complete the paragraph proof to prove that $ab = cd$. given: b is the mid - point of $overline{ac}$, c is the mid - point of $overline{bd}$. prove: $ab = cd$. proof: because b is the mid - point of $overline{ac}$ and select choice is the mid - point of $overline{bd}$, we know by the select choice that $overline{ab}congoverline{bc}$ and $overline{bc}congoverline{cd}$. because congruent segments have select choice measures, $ab = bc$ and select choice. thus, by the select choice, $ab = cd$. need help with this question? get a hint. watch write a paragraph proof

Explanation:

Step1: Identify mid - point property

Since B is the mid - point of $\overline{AC}$ and C is the mid - point of $\overline{BD}$, by the mid - point theorem, we have $\overline{AB}\cong\overline{BC}$ and $\overline{BC}\cong\overline{CD}$.

Step2: Use congruence and equality

Congruent segments have equal measures. So $AB = BC$ and $BC=CD$.

Step3: Apply transitive property

By the transitive property of equality, if $AB = BC$ and $BC = CD$, then $AB = CD$.

Answer:

1. First blank: C
2. Second blank: Mid - point theorem
3. Third blank: equal
4. Fourth blank: $BC = CD$
5. Fifth blank: Transitive property of equality