Question

given: ∠c ≅ ∠l; ∠cbu ≅ ∠lub. prove: cb ≅ lu. how can we show that triangle cbu is congruent to triangle lub? (hint: use the information given and the reflexive poe.) options: asa, sss, aas, sas, there is not enough information given to prove that the triangles are congruent.

Explanation:

Step1: Identify given congruences

We know $\angle C \cong \angle L$, $\angle CBU \cong \angle LUB$, and we can observe that $BU$ is a common side to both $\triangle CBU$ and $\triangle LUB$, so $BU \cong BU$ (reflexive property).

Step2: Match with triangle congruence criterion

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 pairs of congruent angles ($\angle C \cong \angle L$, $\angle CBU \cong \angle LUB$) and a pair of congruent non - included sides ($BU \cong BU$), which fits the AAS criterion.

Answer:

AAS