Prove that triangle ABC and triangle A1B1C1 are equal if angle A is equal to angle A1

Prove that triangle ABC and triangle A1B1C1 are equal if angle A is equal to angle A1, angle B is equal to angle B1, BC is equal to B1C1.

1. We are given that angle A is equal to angle A1, and angle B is equal to angle B1.

2. Since in the triangle ABC the sum of all angles is 180 °, then ∠C = 180 ° – (∠A + ∠B).

3. In triangle A1B1C1 the sum of all angles is also equal to 180 degrees, so C1 = 180 ° – (∠A1 + ∠B1).

4. From this we can conclude that ∠С = ∠С1.

5. Then triangle ABC is equal to triangle A1B1C1 along the side and two adjacent corners (angle B is equal to angle B1, angle C is equal to angle C1, side BC is equal to side B1C1).