Exercise 9 Page 651

Since these are right triangles, we have 5 possible congruence theorem to evaluate SSS Congruence Theorem SAS Congruence Theorem ASA Congruence Theorem AAS Congruence Theorem HL Congruence TheoremIn addition to what we already know, we also see that the triangles share BD as a side. Therefore, we can by the Reflexive Property of Congruence say that this side, or leg as it's called in a right triangle, is congruent as well. Let's add this information to the diagram.

Since we have no information about the triangles second leg, we cannot prove congruence by the SSS Congruence Theorem. This is the only theorem we cannot use though. All other theorems can be used to prove congruence with the given information. For each of the theorems, we have highlighted the relevant parts.