Question

Докажите, что если смежные углы равны, то они прямые

Answer 1

Обозначим равные углы переменной х.
Так как углы смежные, их сумма равна 180°:
х + х = 180°
2х = 180°
х = 90°

То есть равные смежные углы по 90°

Answer 2

Proving that If Adjacent Angles Are Equal, Then They Are Right Angles

To prove that if adjacent angles are equal, then they are right angles, we can use the following reasoning:

1. Definition of Adjacent Angles: - Adjacent angles are angles that have a common vertex and a common side between them.

2. Definition of Right Angles: - Right angles are angles that measure 90 degrees.

3. Given Information: - Let's assume that we have two adjacent angles, A and B, and they are equal in measure.

4. Proof: - If A and B are equal, then their measures can be represented as x degrees each. - Since A and B are adjacent angles, they form a straight line, and the sum of their measures is 180 degrees. - Therefore, if A and B are equal and their sum is 180 degrees, then each angle must measure 90 degrees, which is the definition of a right angle.

5. Conclusion: - Thus, if adjacent angles are equal, then they are right angles.

This proof demonstrates that if two adjacent angles are equal, then they must be right angles.