Question

СРОЧНО!!!№1Дан треугольник в котором стороны относятся как 4:6:7, а стороны другого треугольника равны 24см, 36см, 42см. доказать равенство соответствующих углов этих треугольников.№2 Дан треугольник АВС, угол АВС=90°, BD перпендикулярно AC. AD=9, DC=16.Найти BDрешите любую!!пожалуйста!

Answer 1

Два треугольника имеют равные углы так как отношение соответствующих сторон друг к другу равны т.е.. 24/4=36/6=42/7=6

Answer 2

Task 1: Proving the equality of corresponding angles in two triangles

To prove the equality of corresponding angles in two triangles, we need to compare the ratios of the corresponding sides of the triangles.

Given: - Triangle ABC with side lengths in the ratio 4:6:7 - Another triangle with side lengths 24 cm, 36 cm, and 42 cm

We can start by comparing the ratios of the corresponding sides of the two triangles.

Let's assume that the sides of the first triangle are 4x, 6x, and 7x, where x is a constant.

The sides of the second triangle are given as 24 cm, 36 cm, and 42 cm.

To prove the equality of corresponding angles, we need to show that the ratios of the corresponding sides are equal.

Let's compare the ratios of the corresponding sides:

For the first triangle: - The ratio of the first side to the second side is 4x/6x = 2/3. - The ratio of the second side to the third side is 6x/7x = 6/7.

For the second triangle: - The ratio of the first side to the second side is 24 cm/36 cm = 2/3. - The ratio of the second side to the third side is 36 cm/42 cm = 6/7.

As we can see, the ratios of the corresponding sides in both triangles are equal. Therefore, we can conclude that the corresponding angles in the two triangles are equal.

Task 2: Finding the length of BD

Given: - Triangle ABC with angle ABC = 90° - BD is perpendicular to AC - AD = 9 and DC = 16

To find the length of BD, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, triangle ABC is a right triangle with angle ABC = 90°. Let's label the sides as follows: - AB is the side opposite angle ABC - BC is the side adjacent to angle ABC - AC is the hypotenuse

We are given that AD = 9 and DC = 16. To find the length of BD, we need to find the length of AC.

Using the Pythagorean theorem, we have:

AC^2 = AB^2 + BC^2

Since angle ABC = 90°, we can use the Pythagorean theorem to find the length of AC:

AC^2 = AD^2 + DC^2 AC^2 = 9^2 + 16^2 AC^2 = 81 + 256 AC^2 = 337

Taking the square root of both sides, we find:

AC = √337

Now that we know the length of AC, we can find the length of BD. Since BD is perpendicular to AC, triangle ABD is similar to triangle ABC.

Using the similarity of triangles ABD and ABC, we can set up the following proportion:

BD/AD = BC/AC

Substituting the known values, we have:

BD/9 = BC/√337

To find the length of BD, we can rearrange the equation:

BD = (BC/√337) * 9

However, we don't have the value of BC, so we cannot find the exact length of BD without additional information.

Please provide any additional information you may have, and I'll be happy to assist you further.