Question

Доказать что если биссектрисы двух углов треугольника образуют при пересечении угол 135 градусов, то этот треугольник прямоугольный. Дам 30 баллов если нарисуете с рисунком

Answer 1

Ответ:

Пошаговое объяснение:

Как-то так

Answer 2

Proof that if the bisectors of two angles of a triangle intersect at an angle of 135 degrees, then the triangle is right-angled

To prove that if the bisectors of two angles of a triangle intersect at an angle of 135 degrees, then the triangle is right-angled, we can use the following steps:

1. Let's consider a triangle ABC, where angle A is bisected by the line AD and angle B is bisected by the line BE. 2. The bisectors AD and BE intersect at point O, forming angle AOB. 3. We need to prove that angle AOB is a right angle (90 degrees).

To prove this, we can use the following reasoning:

- The sum of the angles in a triangle is always 180 degrees. - Since angle A is bisected by AD, angles DAB and DAC are equal. - Similarly, since angle B is bisected by BE, angles EBA and EBC are equal.

Now, let's consider the angles formed by the bisectors:

- Angle AOB is formed by the intersection of AD and BE. - Angle DOB is formed by the intersection of AD and OB. - Angle EOA is formed by the intersection of BE and OA.

Since angles DAB and DAC are equal, we can denote them as x. Similarly, angles EBA and EBC can be denoted as y.

Using the reasoning above, we can write the following equations:

1. Angle AOB = 2x + 2y (since it is formed by the intersection of two bisectors) 2. Angle DOB = x + y (since it is formed by the intersection of AD and OB) 3. Angle EOA = x + y (since it is formed by the intersection of BE and OA)

According to the problem statement, angle AOB is 135 degrees. Therefore, we can write the equation:

2x + 2y = 135

To prove that angle AOB is a right angle (90 degrees), we need to show that x + y = 45.

Now, let's solve the equation:

2x + 2y = 135

Dividing both sides by 2:

x + y = 67.5

Since x + y = 67.5, which is not equal to 45, we can conclude that the statement "if the bisectors of two angles of a triangle intersect at an angle of 135 degrees, then the triangle is right-angled" is not true.

Therefore, we cannot prove that the triangle is right-angled based on the given information.

Please note that the given information does not provide enough evidence to prove the statement.