Question

Основания BC и AD трапеции ABCD равны соответсвенно8. И 32 BD=16 докажите ,что треугольники CBD BDA подобны

Answer 1

Рассмотрим треугольник АВД и треугольник ВСД
а)ВД- общая
б)угол А= углу С- противоположные углы
След-но,треугольник АВД  подобен треугольнику  СВД

Answer 2

Given Information

We are given that the bases of trapezoid ABCD, BC and AD, are equal to 8 and 32 respectively. Additionally, we are told that BD is equal to 16.

To Prove

We need to prove that triangles CBD and BDA are similar.

Proof

To prove that triangles CBD and BDA are similar, we need to show that their corresponding angles are equal and their corresponding sides are proportional.

1. Corresponding Angles: We can see that angle CBD and angle BDA are both adjacent to side BD. Since they are adjacent angles formed by intersecting lines, they are vertical angles and therefore equal to each other.

2. Corresponding Sides: We are given that BD is equal to 16. To prove that the corresponding sides are proportional, we need to show that the ratio of the lengths of the sides is the same.

Let's compare the lengths of the sides: - Side CB is equal to the sum of BC and BD, which is 8 + 16 = 24. - Side BA is equal to the difference between AD and BD, which is 32 - 16 = 16.

The ratio of the lengths of the sides is CB/BA = 24/16 = 3/2.

Therefore, we have shown that the corresponding sides are proportional.

Since we have shown that the corresponding angles are equal and the corresponding sides are proportional, we can conclude that triangles CBD and BDA are similar.

Conclusion

We have proven that triangles CBD and BDA are similar.