The congruence of triangles ΔLMO and ΔNOM in parallelogram LMNO is established through the Side-Angle-Side (SAS) criterion, affirming the equality of corresponding angles and sides.
In a parallelogram LMNO, the opposite sides are parallel and equal in length, and the opposite angles are congruent. Let ∠L and ∠N represent the interior angles at vertices L and N, respectively. Since LMNO is a parallelogram, ∠L is congruent to ∠N. Now, consider triangles ΔLMO and ΔNOM.
Side LM is congruent to side NO because they are opposite sides of the parallelogram.
Side MO is common to both triangles.
The angle ∠LMO is congruent to ∠NOM because both are corresponding angles in a parallelogram.
By the Side-Angle-Side (SAS) congruence criterion, we have established that ΔLMO is congruent to ΔNOM. This implies that all corresponding angles and sides are equal, confirming the congruence of the two triangles. Therefore, we have successfully proven that ΔLMO is congruent to ΔNOM in the parallelogram LMNO.