The following triangles are congruent because both show

SAS property

Explanation

From the diagram, you are comparing △ABE and △CBD.

Given from the markings

• AB = BC (single tick mark)

• BE = BD (double tick mark)

• The angle formed between these pairs of equal sides is the vertical angle at B, so
  ∠ABE = ∠CBD (vertical angles are equal)

How to prove the triangles are congruent

Use the SAS Congruence Rule:

1. \( \overline{AB} = \overline{BC} \)

2. Included angle ∠ABE = ∠CBD (vertical angles)

3. \( \overline{BE} = \overline{BD} \)

Conclusion

Since two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle:

△ABE ≅ △CBD by SAS