Question

question given: $overline{ab}congoverline{cd}$ and $overline{bc}congoverline{ad}$. prove: $overline{ac}$ bisects $overline{bd}$. step statement reason 1 $overline{ab}congoverline{cd}$ $overline{bc}congoverline{ad}$ given 2 $overline{ac}congoverline{ac}$ select a reason... note: $overline{ac}$ and $overline{bd}$ are segments. answer attempt 2 out of 2 you must answer all questions above in order to submit.

Explanation:

Step1: State reflexive property

$\overline{AC}\cong\overline{AC}$ by the reflexive property of congruence (any segment is congruent to itself).

Step2: Prove triangle congruence

In $\triangle ABC$ and $\triangle CDA$, we have $\overline{AB}\cong\overline{CD}$ (given), $\overline{BC}\cong\overline{AD}$ (given) and $\overline{AC}\cong\overline{AC}$ (reflexive property). So, $\triangle ABC\cong\triangle CDA$ by the SSS (Side - Side - Side) congruence criterion.

Step3: Use congruent - triangle properties

Since $\triangle ABC\cong\triangle CDA$, $\angle BAC\cong\angle DCA$.

Step4: Prove another pair of triangles congruent

In $\triangle ABE$ and $\triangle CDE$, $\angle BAC\cong\angle DCA$ (from step 3), $\angle AEB\cong\angle CED$ (vertical angles are congruent), and $\overline{AB}\cong\overline{CD}$ (given). So, $\triangle ABE\cong\triangle CDE$ by the AAS (Angle - Angle - Side) congruence criterion.

Step5: Conclude bisection

Since $\triangle ABE\cong\triangle CDE$, $\overline{BE}\cong\overline{DE}$. Hence, $\overline{AC}$ bisects $\overline{BD}$.

Answer:

The proof that $\overline{AC}$ bisects $\overline{BD}$ is completed as above.