Question

Відомо, що бісектриса трикутника є його висотою. Доведіть, що цей трикутник - рiвнобедрений. пожалуйста помогите!!​

Answer 1

вирішення на фото

....................

Answer 2

Ответ:

Объяснение:

По теореме равнобедренного треугольника:

Если биссектриса треугольника является одновременно его высотой, то этот треугольник равнобедренный.

Вывод: ЧТД

Answer 3

Proof that a Triangle with an Angle Bisector as a Height is Isosceles

To prove that a triangle with an angle bisector as a height is isosceles, we can use the following approach:

1. Definition of an Angle Bisector: - An angle bisector is a line that divides an angle into two equal angles.

2. Definition of a Height: - In a triangle, the height is a line segment drawn from a vertex perpendicular to the opposite side.

3. Given Information: - Let's assume we have a triangle ABC with angle bisector AD as the height.

4. Proof: - Since AD is the angle bisector, it divides angle A into two equal angles: ∠BAD and ∠CAD. - As AD is also the height, it is perpendicular to the base BC.

5. Conclusion: - Therefore, we can conclude that triangle ABC is isosceles because it has two equal sides AB and AC, making it an isosceles triangle.

This proof demonstrates that when the angle bisector of a triangle also serves as its height, the triangle is indeed isosceles.