Question

for items 11 - 13, refer to the diagram. if bd bisects ac and ac bisects bd, is △abe≅△cde? explain. a. yes, the triangles are congruent by side - side - angle. b. yes, the triangles are congruent by side - side - side. c. yes, the triangles are congruent by angle - angle - side. d. no, the triangles are not congruent.

Explanation:

Step1: Identify vertical angles

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

Step2: Use the property of bisectors

Since $BD$ bisects $AC$ and $AC$ bisects $BD$, we have $AE = CE$ and $BE=DE$.

Step3: Apply congruence criterion

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

Answer:

A. Yes, the triangles are congruent by Side - Angle - Side.