Question

which of the following relationships proves why $\triangle adb$ and $\triangle ceb$ are congruent?
sss
sas
aas
hl

Explanation:

To determine the congruence of $\triangle ADB$ and $\triangle CEB$, we analyze the given information:

• We know $\overline{AD} \cong \overline{CE}$ (a side), $\angle A \cong \angle C$ (an angle), and $\angle B \cong \angle B$ (another angle).
• The AAS (Angle - Angle - Side) congruence criterion states that if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, then the triangles are congruent. Here, we have two angles ($\angle A\cong\angle C$ and $\angle B\cong\angle B$) and a non - included side ($\overline{AD}\cong\overline{CE}$) that satisfy the AAS condition.
• SSS (Side - Side - Side) requires three pairs of congruent sides, which we don't have enough information for. SAS (Side - Angle - Side) requires two sides and the included angle, but we don't have the included angle here. HL (Hypotenuse - Leg) is for right triangles, and we don't know if these are right triangles.

Answer:

C. AAS