If in triangles ABC and DEF, 𝐴𝐵𝐷𝐸 = 𝐵𝐶𝐹𝐷. Both triangles will be similar when

To determine if triangles ABC and DEF are similar, we need to compare their corresponding angles and side lengths.

Step 1: Compare the corresponding angles:

• We are given that angle ABD is equal to angle BCD (𝐴𝐵𝐷𝐸 = 𝐵𝐶𝐹𝐷).
• We need to check if the other corresponding angles are also equal: angle ABC and angle DEF, as well as angle BCA and angle EFD.

Step 2: Compare the corresponding side lengths:

• We need to check if the ratios of the corresponding side lengths are equal.
• Compare side AB and side DE, side BC and side EF, and side AC and side DF.

If all corresponding angles are equal and the ratios of the corresponding side lengths are equal, then triangles ABC and DEF are similar.