На рисунке ∠OKN = ∠OML = 90°, а OK = OM. Докажите, что OL = ON.

Решение:

Given:

• ∠OKN = ∠OML = 90° (Right angles)
• OK = OM (Given)

To prove: OL = ON

Proof:

Consider the right triangles ONK and OLM:

In triangle ONK:

• ∠OKN = 90° (Given)
• OK = ON (Given)
• Angle ONK = Angle OKN (By definition)

In triangle OLM:

• ∠OML = 90° (Given)
• OM = OL (Given)
• Angle OML = Angle OLM (By definition)

Since OK = OM and the angles are equal, by hypotenuse-leg congruence, the triangles ONK and OLM are congruent.

Therefore, by corresponding parts of congruent triangles, we have:

• ON = OL (Corresponding sides in congruent triangles)

Hence, we have proved that OL = ON.