Question

state how the triangles can be proven congruent, if possible.
∠b ≅ ∠o alt. int. ∠s ≅ ∠bwa ≅ ∠owl vertical ∠s ≅ asa
∠b ≅ ∠o & ∠a ≅ ∠l alt. int. ∠s ≅, aas
∠b ≅ ∠o alt. int. ∠s ≅ ∠bwa ≅ ∠owl vertical ∠s ≅ aas
∠b ≅ ∠o & ∠bwa ≅ ∠owl alt. int. ∠s ≅, asa

Explanation:

Step1: Identify vertical angles

$\angle BWA$ and $\angle OWL$ are vertical angles. By the vertical angles theorem, $\angle BWA\cong\angle OWL$.

Step2: Identify alternate - interior angles

Given that $\angle B\cong\angle O$ (alternate - interior angles). Also, assume the sides between these angles are equal (marked as equal in the figure).

Step3: Apply ASA congruence criterion

The Angle - Side - Angle (ASA) congruence criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Here, $\angle B\cong\angle O$, $\angle BWA\cong\angle OWL$ (vertical angles), and the sides between these angles (the sides marked equal) are congruent.

Answer:

$\angle B\cong\angle O$ alt. int. $\angle s\cong$, $\angle BWA\cong\angle OWL$ vertical $\angle s\cong$, $ASA$