Question

Доказательство теоремы о сумме углов треугольника.Помогите пожалуйста .Кратко и с рисунком. Вот теорема: сумма углов треугольника равна 180

Answer 1

Вот так наверное ,я думаю

Answer 2

Theorem of the Sum of Triangle Angles

The theorem states that the sum of the three interior angles of a triangle is always equal to 180 degrees.

Proof of the Theorem

The proof of this theorem can be demonstrated in various ways, but one of the most common and straightforward methods is by using the properties of parallel lines and transversals.

Consider a triangle ABC, as shown in the diagram below:

     A
    / \
   /   \
  /_____\ 
 B       C

1. Draw a Line Parallel to One Side: Draw a line through point C that is parallel to side AB. This creates a transversal that intersects the lines AB and AC.

2. Use the Properties of Parallel Lines: By the properties of parallel lines and transversals, the alternate interior angles formed are congruent. This means that angle B is congruent to angle C (denoted as ∠B ≅ ∠C).

3. Apply the Property of a Straight Line: Since angle B and angle C are congruent, and together they form a straight line, their sum is 180 degrees (denoted as ∠B + ∠C = 180°).

4. Apply the Triangle Angle Sum Theorem: Since angle A is not involved in the construction, it remains unchanged and is still equal to angle A. Therefore, the sum of the three angles of the triangle ABC is ∠A + ∠B + ∠C = ∠A + 180° = 180°.

Conclusion

This demonstrates that the sum of the interior angles of a triangle is indeed 180 degrees, as per the theorem.