Question

Докажите что биссектрисы внутренних углов при параллельных прямых и секущей образуют прямой угол. Заранее спасибо

Answer 1

Внутренние односторонние углы, образованных двумя параллельными прямыми и секущей, в сумме равны 180°, значит половины этих углов в сумме равны 90°. Таким образом, угол, образованный биссектрисами, равен 180°-90°=90°, что и требовалось доказать.

Answer 2

Proof that the bisectors of the interior angles formed by parallel lines and a transversal create a right angle

To prove that the bisectors of the interior angles formed by parallel lines and a transversal create a right angle, we can use the properties of parallel lines and angles.

Let's consider the following diagram:

          A
         / \
        /   \
       /     \
      /       \
     /_________\
    B           C

In this diagram, lines AB and AC are parallel, and line BC is the transversal. Let's assume that the bisector of angle BAC intersects line BC at point D.

To prove that angle BAD and angle DAC form a right angle, we need to show that they are complementary angles, meaning their sum is equal to 90 degrees.

We can start by proving that angle BAD and angle CAD are congruent. Since the bisector of angle BAC intersects line BC, it divides angle BAC into two congruent angles, angle BAD and angle CAD.

Next, we can prove that angle BAD and angle CAD are supplementary angles. Since lines AB and AC are parallel, angle BAC and angle CAD are corresponding angles, and they are congruent. Therefore, angle BAD and angle CAD are supplementary angles.

Finally, since angle BAD and angle CAD are congruent and supplementary, their sum is equal to 180 degrees. Therefore, each angle measures 90 degrees, and angle BAD and angle CAD form a right angle.

In conclusion, the bisectors of the interior angles formed by parallel lines and a transversal create a right angle.