Question

Помогите пожайлуста,сил уже нет никаких.......Отрезки МК и РН пересекаются в точке О,являющейся серединой отрезка МК. Докажите,что угол МРО= углу КНО, если угол РМО = равен углу НКО.

Answer 1

Углы ∠PMO=∠HKO по условию, углы ∠POM=∠HOK, как вертикальные, MO=OK по условию, значит, ΔPOM=ΔHOK по стороне и двум прилежащим к ней углам, знаит, ∠MPO=∠KHO

Answer 2

Proof that angle MRO is equal to angle KNO

To prove that angle MRO is equal to angle KNO, given that angle RMO is equal to angle NKO, we can use the fact that O is the midpoint of segment MK.

Let's consider the triangles MRO and KNO. We know that angle RMO is equal to angle NKO (given), and we want to prove that angle MRO is equal to angle KNO.

Since O is the midpoint of segment MK, we can conclude that segment MO is equal to segment KO and segment RO is equal to segment NO.

Now, let's consider the two triangles MRO and KNO. We have:

- Segment MO is equal to segment KO (O is the midpoint of MK). - Segment RO is equal to segment NO (O is the midpoint of MK). - Angle RMO is equal to angle NKO (given).

By the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle MRO is congruent to triangle KNO.

When two triangles are congruent, their corresponding angles are equal. Therefore, angle MRO is equal to angle KNO.

Hence, we have proved that angle MRO is equal to angle KNO, given that angle RMO is equal to angle NKO.

Please let me know if you need any further clarification or assistance!