1. **State the problem:** Determine if triangles $\triangle ADE$ and $\triangle BEC$ are similar by AA similarity and find the correct similarity statement. 2. **Recall AA similarity rule:** Two triangles are similar if two pairs of corresponding angles are equal. 3. **Given angles:** - $\triangle ADE$ has angles $78^\circ$, $45^\circ$, and the third angle is $180^\circ - 78^\circ - 45^\circ = 57^\circ$. - $\triangle BEC$ has two angles given as $45^\circ$ and $45^\circ$, so the third angle is $180^\circ - 45^\circ - 45^\circ = 90^\circ$. 4. **Compare angles:** - $\triangle ADE$ angles: $78^\circ$, $45^\circ$, $57^\circ$ - $\triangle BEC$ angles: $45^\circ$, $45^\circ$, $90^\circ$ No two angles match between the triangles except one $45^\circ$ angle. 5. **Conclusion:** Since only one pair of angles matches, the triangles are **not similar by AA similarity**. **Final answer:** D not similar by AA