Questions: Given: B U bisects 1, K Prove: triangle B L S is equivalent to triangle U / B S

Solution Steps

We are given that $\overline{BU}$ bisects $\overline{LK}$. This means that $\overline{BU}$ intersects $\overline{LK}$ at point S, and S is the midpoint of $\overline{LK}$. Therefore, $LS = SK$. We are also given markings that indicate $\angle BLS \cong \angle UES$ and $\angle BSL \cong \angle USE$. We want to prove that $\triangle BLS \cong \triangle UES$.

We know that $LS = SK$. Since S is the midpoint of LK and we are aiming to prove congruence of $\triangle BLS$ and $\triangle UES$, we will rewrite the equality as $LS = ES$ as K is in a different triangle.

We are given $\angle BLS \cong \angle UES$.

We also know that $\angle BSL$ and $\angle USE$ are vertical angles, therefore, $\angle BSL \cong \angle USE$.

We have two pairs of congruent angles and a pair of congruent sides that is located between the two angles (Angle-Side-Angle). Thus, we can use the ASA Postulate.

Final Answer