Question

Отрезки AB и CD пересекаются в точке O так, что AO = OC и BO = DO. Докажите, что угол ABC = углу BDC помогите

Answer 1

Треугольник AОС- равнобедренный, значит угол А = углу С
угол С=углу D (как накрест-лежащие)
угол В=углу А (как накрест-лежащие)
т.к. угол А = углу С, соответственно, угол В=углу D
чтд

Answer 2

Given Information:

We are given that line segments AB and CD intersect at point O such that AO = OC and BO = DO.

To Prove:

We need to prove that angle ABC is equal to angle BDC.

Proof:

To prove that angle ABC is equal to angle BDC, we can use the following steps:

1. Since AO = OC and BO = DO, we can conclude that triangles AOB and COD are congruent by the Side-Angle-Side (SAS) congruence criterion. - Source: 2. By the congruence of triangles AOB and COD, we can conclude that angle ABO is equal to angle CDO and angle BAO is equal to angle DCO. - Source: 3. Since angle ABO is equal to angle CDO and angle BAO is equal to angle DCO, we can add these angles to get: angle ABC = angle ABO + angle BAO = angle CDO + angle DCO = angle BDC.

Therefore, we have proved that angle ABC is equal to angle BDC.