From the given figure, let's determine if the triangles below are congruent.
From the given triangle, two pairs of sides are already shown to be congruent.
Also, by applying the Vertical Angles Theorem, the vertical angles are congruent.
The vertical angles theorem states that the angles formed by two intersecting lines are which are the vertical angles are congruent.
Therefore, we can say the triangles are congruent by applying by Side-Angle-Side (SAS) theorem.
The SAS theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then both triangles are congruent.
ANSWER:
The triangles are congruent using the SAS theorem.