Question

In the figure below, it is given that ⎯⎯⎯⎯⎯⎯≅.To prove triangle BCD ≅ triangle CBE by the SSS Congruence Theorem, what additional information is sufficient?

Answer 1

To use the SSS Congruence Theorem, we need to have all the 3 corresponding sides of each triangle equal. From the text, we already know BD and CE are congruent. Those triangles share the side BC, then we already know they are congruent(since it is the same segment). We already have the congruence for 2 sides, we just need the congruence for the last side of each triangle which is the following relation

`DC\cong EB`

With this we can use the SSS Congruence Theorem.