Question

Докажите что биссектриса проведённая к основанию равнобедренного треугольника разбивает его на два равных треугольника.

Answer 1

Это доказывается по 3 сторонам, Все три стороны будут равны ( один угол общий, а двое других равны по условию) 

Answer 2

Proof that the Bisector Drawn to the Base of an Isosceles Triangle Divides it into Two Equal Triangles

To prove that the bisector drawn to the base of an isosceles triangle divides it into two equal triangles, we can use the following reasoning:

1. Definition of an Isosceles Triangle: - An isosceles triangle is a triangle that has at least two sides of equal length.

2. Bisector of the Base: - When a bisector is drawn to the base of an isosceles triangle, it divides the base into two equal segments.

3. The Bisector Divides the Opposite Angle Equally: - The bisector also divides the opposite angle into two equal angles.

4. Application of the Angle Bisector Theorem: - According to the Angle Bisector Theorem, the angle bisector in a triangle divides the opposite side in the same ratio as the other two sides of the triangle.

5. Conclusion: - Therefore, since the bisector divides both the base and the opposite angle equally, it follows that the two resulting triangles are equal in size.

This reasoning demonstrates that the bisector drawn to the base of an isosceles triangle indeed divides it into two equal triangles.