Question

Помогите!!!Теорема о смежных углах с доказательством

Answer 1

два угла у которых, одна сторона  общая, а другие являются продолжением одна другой, называються смежными. на рисунке (думаю сама сможешь сделать) углы АОВ и ВОС смежные( из определения).т.к лучи ОАи ОС образуют развернутый угол, то: угол АОВ + угол ВОС = углу АОС = 180градусам. следовательно, сумма смежных углов равна 180 градусам.

Answer 2

Theorem on Vertical Angles (Теорема о смежных углах)

The theorem on vertical angles states that when two lines intersect, the pairs of opposite angles formed are congruent. In other words, vertical angles are equal in measure.

Proof: To prove this theorem, let's consider two lines, line AB and line CD, intersecting at point O. This forms four angles: ∠AOC, ∠COB, ∠BOD, and ∠DOA.

We need to show that ∠AOC is congruent to ∠BOD and ∠COB is congruent to ∠DOA.

Using the properties of angles formed by intersecting lines, we can write the following equations:

∠AOC + ∠COB = 180° (linear pair) ∠BOD + ∠DOA = 180° (linear pair)

From these equations, we can see that ∠AOC and ∠BOD are supplementary angles, as are ∠COB and ∠DOA.

Since supplementary angles have a sum of 180°, we can conclude that ∠AOC is congruent to ∠BOD and ∠COB is congruent to ∠DOA.

Therefore, the theorem on vertical angles is proven.