Question

Помогите пожалуйста Задача 1. Докажите подобие треугольников АВС и NМР, если угол А равен углу N и равно 72 градуса. АВ = 12; АС = 9; NM = 8, NP = 6. Задача 2. Докажите подобие треугольников АВС и NMP, если АВ = 12; ВС = 16; АС = 24; NM = 6; MP = 8, NP = 12.​

Answer 1

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Answer 2

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Answer 3

Task 1: Proving the similarity of triangles ABC and NMR

To prove the similarity of triangles ABC and NMR, we need to show that their corresponding angles are equal and their corresponding sides are proportional.

Given information: - Angle A is equal to angle N and both are equal to 72 degrees. - Side AB is equal to 12 units. - Side AC is equal to 9 units. - Side NM is equal to 8 units. - Side NP is equal to 6 units.

To prove the similarity, we will compare the corresponding angles and sides:

1. Corresponding angles: - Angle A is equal to angle N (given). - Angle B is equal to angle M (since the sum of angles in a triangle is 180 degrees). - Angle C is equal to angle R (since the sum of angles in a triangle is 180 degrees).

2. Corresponding sides: - Side AB corresponds to side NM. - Side AC corresponds to side NP.

Now, let's compare the ratios of the corresponding sides:

- Ratio of AB to NM: AB/NM = 12/8 = 3/2. - Ratio of AC to NP: AC/NP = 9/6 = 3/2.

Since the ratios of the corresponding sides are equal, and the corresponding angles are equal, we can conclude that triangles ABC and NMR are similar.

Task 2: Proving the similarity of triangles ABC and NMP

To prove the similarity of triangles ABC and NMP, we need to show that their corresponding angles are equal and their corresponding sides are proportional.

Given information: - Side AB is equal to 12 units. - Side BC is equal to 16 units. - Side AC is equal to 24 units. - Side NM is equal to 6 units. - Side MP is equal to 8 units. - Side NP is equal to 12 units.

To prove the similarity, we will compare the corresponding angles and sides:

1. Corresponding angles: - Angle A is equal to angle N (given). - Angle B is equal to angle M (since the sum of angles in a triangle is 180 degrees). - Angle C is equal to angle P (since the sum of angles in a triangle is 180 degrees).

2. Corresponding sides: - Side AB corresponds to side NM. - Side BC corresponds to side MP. - Side AC corresponds to side NP.

Now, let's compare the ratios of the corresponding sides:

- Ratio of AB to NM: AB/NM = 12/6 = 2. - Ratio of BC to MP: BC/MP = 16/8 = 2. - Ratio of AC to NP: AC/NP = 24/12 = 2.

Since the ratios of the corresponding sides are equal, and the corresponding angles are equal, we can conclude that triangles ABC and NMP are similar.

In both tasks, we have shown that the corresponding angles are equal and the corresponding sides are proportional, which proves the similarity of the given triangles.