Answer
1) $\angle A$ is the common angle. $\overline{AB}$ is the common side.
2) If $\overline{BC}\cong\overline{BD}$, we cannot conclude that $\triangle ABC$ and $\triangle ABD$ are congruent.
3) SSA is not a reason to prove 2 triangles congruent.
Work Step by Step
1) A common angle is the angle that both triangles have. In the image, we see that both triangles $\triangle ABC$ and $\triangle ABD$ share the angle $\angle A$. So. $\angle A$ is the common angle.
Similary, a common side is the side that both triangles have. Here, both triangles share the side $\overline{AB}$. Therefore, $\overline{AB}$ is the common side.
2) There are 4 ways to prove that 2 triangles are congruent: SSS, SAS, ASA and AAS (which is actually ASA).
Here, since both triangles $\triangle ABC$ and $\triangle ABD$ have common angle $\angle A$ and common side $\overline{AB}$, we need either of the following to get congruence:
- $\overline{AC}\cong\overline{AD}$ to have SAS
- $\angle ABC\cong\angle ABD$ to have ASA
- $\angle ACB\cong\angle ADB$ to have AAS.
Instead, having $\overline{BC}\cong\overline{BD}$ means we only have SSA, which is not enough to prove 2 triangles are congruent.
3) As said above, SSA is not a reason to prove triangles congruent.
To prove that, we can refer to Figure 3.9 in the textbook to show an example where 2 triangles have SSA but are not congruent.
