На рисунке 4 𝐴𝐶 = 𝐵𝐷. Докажите, что 𝐴𝐵 = 𝐶𝐷.

To prove that 𝐴𝐵 = 𝐶𝐷, we need to use the fact that 𝐴𝐶 = 𝐵𝐷.

Given that 𝐴𝐶 = 𝐵𝐷, we can consider the two triangles 𝐴𝐵𝐶 and 𝐶𝐷𝐵.

By the side-angle-side (SAS) congruence, we can prove that both triangles are congruent.

1. 𝐴𝐶 = 𝐵𝐷 (Given).
2. 𝐵𝐶 = 𝐶𝐵 (Common side).
3. ∠𝐶𝐴𝐵 = ∠𝐷𝐵𝐶 (Vertical angles).

Using these two congruent triangles, we know that the corresponding sides are equal.

So, 𝐴𝐵 = 𝐶𝐷.

Therefore, we have proved that 𝐴𝐵 = 𝐶𝐷.