Question

proof prove △abc ≅ △edc by dragging the statements into the correct order. given: ab ≅ ed, ca ≅ ce, ac bisects bd. prove: △abc ≅ △edc proof: keyboard help △abc ≅ △edc (sss) ab ≅ ed, ca ≅ ce, ac bisects bd (given) c is the midpoint of bd. (definition of segment bisector) bc ≅ cd (midpoint theorem)

Explanation:

Step 1: Start with Given Information

We begin by stating the given information: $\overline{AB} \cong \overline{ED}$, $\overline{CA} \cong \overline{CE}$, and $\overline{AC}$ bisects $\overline{BD}$. This provides the initial congruent sides and the bisector condition.

Step 2: Define Midpoint from Bisector

Since $\overline{AC}$ bisects $\overline{BD}$, by the definition of a segment bisector, $C$ must be the midpoint of $\overline{BD}$. This means $C$ divides $\overline{BD}$ into two equal parts.

Step 3: Apply Midpoint Theorem

By the Midpoint Theorem, if $C$ is the midpoint of $\overline{BD}$, then $\overline{BC} \cong \overline{CD}$. This gives us the third pair of congruent sides needed for the SSS (Side - Side - Side) congruence criterion.

Step 4: Conclude Triangle Congruence

Now we have three pairs of congruent sides: $\overline{AB} \cong \overline{ED}$, $\overline{CA} \cong \overline{CE}$, and $\overline{BC} \cong \overline{CD}$. By the SSS congruence postulate, we can conclude that $\triangle ABC \cong \triangle EDC$.

Answer:

The correct order of statements for the proof is:

1. $\overline{AB} \cong \overline{ED}, \overline{CA} \cong \overline{CE}, \overline{AC}$ bisects $\overline{BD}$ (Given)
2. $C$ is the midpoint of $\overline{BD}$ (Definition of segment bisector)
3. $\overline{BC} \cong \overline{CD}$ (Midpoint Theorem)
4. $\triangle ABC \cong \triangle EDC$ (SSS)