Question

Докажите,что в равных треугольниках биссектрисы,проведённые к соответственно равным сторонам,равны. Хочу проверить правильным ли я путём пошёл. Решил в одно действие. Пишите все,как думаете!!! Пожалуйста!

Answer 1

Естественно равны, биссектриса-это линия, которая делит УГОЛ на две равные части. В данном случае Медиана, но ничего страшного я не вижу. Дак вот ,ближе к делу.
Если биссектрисы проведены, как ты утверждаешь К СООТВЕТСТВЕННО РАВНЫМ СТОРОНАМ, то какие еще вопросы могут быть?!?!

Answer 2

Proof that the bisectors drawn to the corresponding sides of congruent triangles are equal

To prove that the bisectors drawn to the corresponding sides of congruent triangles are equal, we can use the following steps:

1. Consider two congruent triangles, ΔABC and ΔDEF, where AB = DE, BC = EF, and AC = DF. We want to prove that the bisectors drawn to the corresponding sides of these triangles are equal.

2. Let the bisector of angle A in ΔABC be AD, and the bisector of angle D in ΔDEF be DG.

3. To prove that AD = DG, we need to show that the lengths of AD and DG are equal.

4. Since ΔABC and ΔDEF are congruent, their corresponding angles are equal. Therefore, angle A = angle D.

5. By the angle bisector theorem, we know that the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the lengths of the opposite sides. In other words, AD/BD = DG/EF.

6. Since AB = DE and BC = EF, we can substitute these values into the equation from step 5 to get AD/BD = DG/EF.

7. Since AB = DE and AC = DF, we can also substitute these values into the equation from step 5 to get AD/CD = DG/DF.

8. Combining the equations from steps 6 and 7, we have AD/BD = DG/EF = AD/CD = DG/DF.

9. From the equation AD/BD = DG/EF, we can cross-multiply to get AD * EF = DG * BD.

10. Similarly, from the equation AD/CD = DG/DF, we can cross-multiply to get AD * DF = DG * CD.

11. Subtracting the equation from step 10 from the equation from step 9, we have AD * EF - AD * DF = DG * BD - DG * CD.

12. Factoring out AD from the left side of the equation and DG from the right side of the equation, we have AD * (EF - DF) = DG * (BD - CD).

13. Since AB = DE and BC = EF, we can substitute these values into the equation AD * (EF - DF) = DG * (BD - CD) to get AD * (BC - DF) = DG * (BD - CD).

14. Since BC = EF and AC = DF, we can also substitute these values into the equation AD * (BC - DF) = DG * (BD - CD) to get AD * AC = DG * BD.

15. Dividing both sides of the equation AD * AC = DG * BD by AC, we have AD = DG * BD/AC.

16. Since ΔABC and ΔDEF are congruent, AC = DF. Therefore, we can substitute this value into the equation AD = DG * BD/AC to get AD = DG * BD/DF.

17. Since AB = DE, we can also substitute this value into the equation AD = DG * BD/DF to get AD = DG * AB/DF.

18. Since AB = DE and AC = DF, we can substitute these values into the equation AD = DG * AB/DF to get AD = DG.

19. Therefore, we have proved that the bisectors drawn to the corresponding sides of congruent triangles are equal.

Note: The above proof is based on the properties of congruent triangles and the angle bisector theorem. It is important to note that the proof provided here is a general proof and may not be specific to the sources provided.