In the four-sided figure ABCD, AB = AD and the line AC bisects the angle BAD…

Step 1. The triangles. Take $\triangle ABC$ and $\triangle ADC$.

Step 2. The equal parts.

1. $AB = AD$, given.
2. $\angle BAC = \angle DAC$, because $AC$ bisects $\angle BAD$.
3. $AC = AC$, the common side.

Step 3. The rule. $\triangle ABC \cong \triangle ADC$ by SAS. So $BC = DC$ by CPCT.

Step 4. The perimeter. $CD = BC = 9\ \text{cm}$ and $DA = AB = 7\ \text{cm}$. The perimeter is $7 + 9 + 9 + 7 = 32\ \text{cm}$.