To show that triangle ABC is congruent to triangle DEF, we can use the concept of congruent triangles and the corresponding parts of congruent triangles (CPCTC) theorem.
Start by identifying the corresponding angles and sides of the two triangles. For example, angle A in triangle ABC corresponds to angle D in triangle DEF, angle B corresponds to angle E, and angle C corresponds to angle F. Similarly, side AB corresponds to side DE, side BC corresponds to side EF, and side AC corresponds to side DF.
Next, we can examine the relationships between the corresponding angles and sides. If we can prove that the corresponding angles are congruent and the corresponding sides are equal in length, we can conclude that the triangles are congruent.
Use the properties of angles to establish congruence. For example, if we can show that angle A is congruent to angle D (using the concept of alternate interior angles or same side interior angles), angle B is congruent to angle E, and angle C is congruent to angle F, we have established the congruence of corresponding angles.
Use the properties of sides to establish equality. If we can show that side AB is equal in length to side DE, side BC is equal to side EF, and side AC is equal to side DF, we have established the congruence of corresponding sides.
Finally, apply the corresponding parts of congruent triangles (CPCTC) theorem, which states that if the corresponding parts of two triangles are congruent, then the triangles themselves are congruent. In this case, by showing that the corresponding angles and sides of triangle ABC and triangle DEF are congruent, we can conclude that the triangles are congruent.
By carefully examining the relationships between the angles and sides of the two triangles and using the vocabulary terms such as alternate interior angles, same side interior angles, and corresponding parts, we can demonstrate the congruence of triangle ABC and triangle DEF.