Question

refer to the diagram shown. if $overline{bd}$ bisects $overline{ac}$ and $overline{ac}$ bisects $overline{bd}$, the choose theorem can be used to show that $\triangle abecong\triangle cde$

Explanation:

Step1: Identify equal - length sides

Since $\overline{BD}$ bisects $\overline{AC}$ and $\overline{AC}$ bisects $\overline{BD}$, we have $AE = CE$ and $BE=DE$.

Step2: Identify vertical angles

$\angle AEB$ and $\angle CED$ are vertical angles, so $\angle AEB=\angle CED$.

Step3: Apply congruence theorem

By the Side - Angle - Side (SAS) congruence theorem, since we have two pairs of equal sides ($AE = CE$, $BE = DE$) and the included angles are equal ($\angle AEB=\angle CED$), $\triangle ABE\cong\triangle CDE$.

Answer:

Side - Angle - Side (SAS)