Question

proof write a paragraph proof to prove that if e is the midpoint of $overline{bd}$ and $overline{ac}$, and $be = 2ae$, then $ed = 2ec$. given: e is the midpoint of $overline{bd}$ and $overline{ac}$, and $be = 2ae$. prove: $ed = 2ec$. proof: because e is the midpoint of $overline{bd}$ and $overline{ac}$, we know by the select choice that $overline{be}cong$ select choice and $overline{ae}congoverline{ec}$. because congruent segments have equal measures, $be = ed$ and $ae = ec$. since $be = 2ae$, by the substitution property of equality, $ed = 2ec$. need help with this question? get a hint show answer

Explanation:

Step1: Use mid - point property

Since E is the mid - point of $\overline{BD}$ and $\overline{AC}$, by the definition of a mid - point, we have $\overline{BE}\cong\overline{ED}$ and $\overline{AE}\cong\overline{EC}$. In terms of lengths, $BE = ED$ and $AE=EC$.

Step2: Apply given relation

We are given that $BE = 2AE$.

Step3: Substitute equal lengths

Substitute $BE$ with $ED$ and $AE$ with $EC$ (from Step 1) into the equation $BE = 2AE$. We get $ED = 2EC$ by the substitution property of equality.

Answer:

The proof is completed as shown above. We used the definition of a mid - point to establish equal - length segments and then used the substitution property of equality to prove that if $E$ is the mid - point of $\overline{BD}$ and $\overline{AC}$ and $BE = 2AE$, then $ED = 2EC$.